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Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature.Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrodinger operators, operators on graphs, and the spectral theory of Riemannian manifolds.Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. 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The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, explained in a concise, yet fairly rigorous presentation.Topics and Features:          Fourier series and transforms fundamentally important in random signal analysis and processing are developed from scratch, emphasizing the time-domain vs. frequency-domain duality;          Basic concepts of probability theory, laws of large numbers, the central limit theorem, and statistical parametric inference procedures are presented so that no prior knowledge of probability and statistics is required; the only prerequisite is a basic two three semester calculus sequence;          Computer simulation algorithms of stationary random signals with a given power spectrum density;          Complementary bibliography for readers who wish to pursue the study of random signals in greater depth;          Many diverse examples and end-of-chapter problems and exercises.Developed by the author over the course of many years of classroom use, A First Course in Statistics for Signal Analysis, Second Edition may be used by junior\/senior undergraduates or graduate students in electrical, systems, computer, and biomedical engineering, as well as the physical sciences. The work is also an excellent resource of educational and training material for scientists and engineers working in research laboratories. This third edition contains two additional chapters that present wavelets and the uncertainty principle, and the forecasting problems for stationary time series. These two topics are essential for students to attain a deeper understanding of statistical analysis of random signals.Reviews from previous editions:A First Course in Statistics for Signal Analysis is a small, dense, and inexpensive book that covers exactly what the title says: statistics for signal analysis. The book has much to recommend it. The author clearly understands the topics presented. The topics are covered in a rigorous manner, but not so rigorous as to be ostentatious.  JASA (Review of the First Edition)This is a nicely written self-contained book and it is a good candidate for adoption as a textbook for upper-level undergraduate and even for a graduate course for engineering and physical sciences students. 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It provides a detailed derivation of the asymptotic formulas for Bloch eigenvalues and Bloch functions in arbitrary dimensions while constructing and estimating the measure of the iso-energetic surfaces in the high-energy regime. Moreover, it presents a unique method proving the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed, it determines the spectral invariants of the multidimensional operator from the given Bloch eigenvalues. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential, making it possible to determine the potential constructively using Bloch eigenvalues as input data. Lastly, the book presents an algorithm for the unique determination of the potential.This updated and significantly expanded third edition features an extension of this framework to all dimensions, offering a now complete theory of self-adjoint Schrodinger operators within periodic potentials. Drawing from recent advancements in mathematical analysis, this edition delves even deeper into the intricacies of the subject. It explores the connections between the multidimensional Schrodinger operator, periodic potentials, and other fundamental areas of mathematical physics. 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Motivating examples from the physical sciences, engineering, and economics complete this integrated approach.A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses onfinite difference and finite element methods. Computer-aided calculation with Maple completes the book. Throughout, three fundamental examples are studied with different tools: Poisson s equation, the heat equation, and the wave equation on Euclidean domains. The Black Scholes equation from mathematical finance is one of several opportunities for extension.Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. 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Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book.Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader.A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. 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The author demonstrates how the concept of reproducing kernel Hilbert Spaces (RKHS), accompanied with tools from regularization theory, can be effectively used in the design and justification of kernel learning algorithms, which can address problems in several areas of artificial intelligence. Also provided is a detailed description of two biomedical applications of the considered algorithms, demonstrating how close the theory is to being practically implemented. Among the book’s several unique features is its analysis of a large class of algorithms of the Learning Theory that essentially comprise every linear regularization scheme, including Tikhonov regularization as a specific case. It also provides a methodology for analyzing not only different supervised learning problems, such as regression or ranking, but also different learning scenarios, such as unsupervised domain adaptation or reinforcement learning. 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Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results.  A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics. Sparsity promoting regularization is examined in detail from a Banach space point of view. 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Das Buch richtet sich in erster Linie an Wissenschaftler, Fachleute in Forschungsbereichen der Industrie und fortgeschrittene Studierende der Physik, der angewandten Mathematik und der Ingenieurwissenschaften.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52911166947607,"sku":null,"price":4047.97,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783031262876.jpg?v=1781262231"},{"product_id":"lecture-notes-in-mathematics-9783319924175","title":"Lecture Notes in Mathematics","description":"\u003cp\u003eThe subject of this book stands at the crossroads of ergodic theory and measurable dynamics. With an emphasis on irreversible systems, the text presents a framework of multi-resolutions tailored for the study of endomorphisms, beginning with a systematic look at the latter. 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There is also a non-commutative version: While the study of automorphisms of von Neumann algebras dates back to von Neumann, the systematic study of their endomorphisms is more recent; together with the results in the main text, the book includes a review of recent related research papers, some by the co-authors and their collaborators.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52911233007895,"sku":null,"price":4722.86,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319924175.jpg?v=1781263861"},{"product_id":"bilinear-maps-and-tensor-products-in-operator-theory-9783031340932","title":"Bilinear Maps and Tensor Products in Operator Theory","description":"\u003cp\u003eThis text covers a first course in bilinear maps and tensor products intending to bring the reader from the beginning of functional analysis to the frontiers of exploration with tensor products. 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The book brings the theory of tensor products on Banach spaces to the edges of Grothendieck''s theory, and changes the target towards tensor products of bounded linear operators. Both Hilbert-space and Banach-space operator theory are considered and compared from the point of view of tensor products. This is done from the first principles of functional analysis up to current research topics, with complete and detailed proofs. The first four chapters deal with the algebraic theory of linear spaces, providing various representations of the algebraic tensor product defined in an axiomatic way. Chapters 5 and 6 give the necessary background concerning normed spaces and bounded bilinear mappings. Chapter 7 is devoted to the study of reasonable crossnorms on tensor product spaces, discussing in detail the important extreme realizations of injective and projective tensor products. 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The topics such as the representation of signals, convolution, Fourier Series and Fourier Transform, Laplace transform, Z-transform, and state-space analysis are explained with a large number of numerical examples in the book. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in electrical engineering and related courses.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52911245656343,"sku":null,"price":13430.27,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030757427.jpg?v=1781264221"},{"product_id":"upper-and-lower-bounds-for-stochastic-processes-9783030825959","title":"Upper and Lower Bounds for Stochastic Processes","description":"\u003cp\u003eThis book provides an in-depth account of modern methods used to bound the supremum of stochastic processes. 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The variety of topics covered offers researchers an overview of problems in mechanics that can be analyzed with variational techniques, making this a valuable reference for researchers in the field. It also presents ideas for possible future areas of research, showing how the mastery of these foundational mathematical techniques can be used for many exciting applications. 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From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets – can be successfully applied to mathematical path integrals, leading to remarkable results and paving the wayto a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical\/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52911459172631,"sku":null,"price":7422.41,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783031061868.jpg?v=1781270499"},{"product_id":"springer-optimization-and-its-applications-9783319599939","title":"Springer Optimization and Its Applications","description":"\u003cp\u003eThis textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models.  Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations.The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions.  Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directionalderivatives and expansions of multivariable functions). Illustrative examples, input-output process, optimal recovery of functions and approximations are given; each section lists an ample number of exercises to heighten understanding of the material. Chapter three  discusses deterministic\/mathematical and optimization models evolving from differential equations, difference equations, algebraic models, power function models, input-output models and pathway models. Fractional integral and derivative models are examined.  Chapter four covers non-deterministic\/stochastic models. The random walk model, branching process model, birth and death process model, time series models, and regression type models are examined. The fifth chapter covers optimal design. General linear models from a statistical point of view are introduced; the Gauss-Markov theorem, quadratic forms, and generalized inverses of matrices are covered. 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An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com\/springer-math\/adventures-in-graph-theory. The text is geared towards advanced undergraduate and graduate students and is particularly useful for those trying to decide what type of problem to tackle for their dissertation. 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Topics include: Fixed point theory Fixed-circle theory Coupled fixed points Nonlinear duality in Banach spaces Jensen''s integral inequality and applications Nonlinear differential equations Nonlinear integro-differential equations Quasiconvexity, Stability of a Cauchy-Jensen additive mapping Generalizations of metric spaces Hilbert-type integral inequality, Solitons Quadratic functional equations in fuzzy Banach spaces Asymptotic orbits in Hill’sproblem Time-domain electromagnetics Inertial Mann algorithms Mathematical modelling RoboticsGraduate students and researchers will find this book helpful in comprehending current applications and developments in mathematical analysis. 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Special care is taken to analyze the difficult cases of non-smooth interfaces which are not completely enclosed in one subdomain, i.e, intersect with the outer boundary. This can hardly be found in the literature. 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Recommended for postgraduate students and early career researchers who aim to acquire knowledge in this area in preparation for further research, this book is also suitable for established researchers aiming to get up to speed with recent developments in the area, and may very well be used as a guide for further study.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52914865144087,"sku":null,"price":12080.49,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030048075.jpg?v=1781511177"},{"product_id":"partition-functions-and-automorphic-forms-9783030424008","title":"Partition Functions and Automorphic Forms","description":"\u003cp\u003eThis book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. 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The Kato inequality, the Kato type matrix limit theorem, the Howland–Kato commutator problem, the Kato-class of potentials, and the Trotter–Kato product formulae are discussed and analyzed.  Graduate students, research mathematicians, and applied scientists will find that this book provides comprehensive insight into the significance of Tosio Kato’s impact to research in analysis and operator theory.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52914989629719,"sku":null,"price":16129.82,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030126612.jpg?v=1781512019"},{"product_id":"harmonic-balance-for-nonlinear-vibration-problems-9783030140236","title":"Harmonic Balance for Nonlinear Vibration Problems","description":"\u003cp\u003eThis monograph presents an introduction to Harmonic Balance for nonlinear vibration problems, covering the theoretical basis, its application to mechanical systems, and its computational implementation. 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Beginning with an elementary introduction to the topic, including examples accessible to readers without prior knowledge of advanced mathematics, the book''s first five chapters contain a thorough exposition of the most classical results, such as Calderón''s and Hörmander''s theorems. Later chapters explore a selection of results of the last four decades around the themes of continuation for elliptic equations, with the Jerison-Kenig estimates for strong unique continuation, counterexamples to Cauchy uniqueness of Cohen and Alinhac \u0026amp; Baouendi, operators with partially analytic coefficients with intermediate results betweenHolmgren''s and Hörmander''s uniqueness theorems, Wolff''s modification of Carleman''s method, conditional pseudo-convexity, and more. 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A final section containing 50 problems, many of which include helpful hints, rounds out the coverage. Intended for Master’s and PhD students in Mathematics or, more generally, mathematically oriented subjects, the book is designed to be largely self-contained, although some mathematical background is needed: readers should be familiar with measure theory, Banach and Hilbert spaces, locally convex topological vector spaces and, in general, with linear functional analysis.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52915051856151,"sku":null,"price":6072.63,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030196707.jpg?v=1781525411"},{"product_id":"modern-methods-in-operator-theory-and-harmonic-analysis-9783030267483","title":"Modern Methods in Operator Theory and Harmonic Analysis","description":"\u003cp\u003eThis proceedings volume gathers selected, peer-reviewed papers from the \"Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII\" (OTHA 2018) conference, which was held in Rostov-on-Don, Russia, in April 2018. 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Memory functions appear in the formalism of the generalized master equations that express the time evolution of probabilities via equations non-local in time, projection operators allow the extraction of parts of quantities, such as the diagonal parts of density matrices in statistical mechanics, and the defect technique allows solution of transport equations in which the translational invariance is broken in small regions, such as when crystals are doped with impurities. These three methods combined form an immensely useful toolkit for investigations in such disparate areas of physics as excitation in molecular crystals, sensitized luminescence, charge transport, non-equilibrium statistical physics, vibrational relaxation, granular materials, NMR, and even theoretical ecology. This book explains the three techniques and their interrelated nature, along with plenty of illustrative examples. 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