Автор: Dyke, P. P. G. Название: An Introduction to Laplace transforms and Fourier series ISBN: 1852330155 ISBN-13(EAN): 9781852330156 Издательство: Springer Рейтинг: Цена: 32560.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction.
Автор: Saitoh Название: Theory of Reproducing Kernels and Applications ISBN: 981100529X ISBN-13(EAN): 9789811005299 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This book provides a large extension of the general theory of reproducing kernels published by N. Aronszajn in 1950, with many concrete applications.
In Chapter 1, many concrete reproducing kernels are first introduced with detailed information. Chapter 2 presents a general and global theory of reproducing kernels with basic applications in a self-contained way. Many fundamental operations among reproducing kernel Hilbert spaces are dealt with. Chapter 2 is the heart of this book.
Chapter 3 is devoted to the Tikhonov regularization using the theory of reproducing kernels with applications to numerical and practical solutions of bounded linear operator equations.
In Chapter 4, the numerical real inversion formulas of the Laplace transform are presented by applying the Tikhonov regularization, where the reproducing kernels play a key role in the results.
Chapter 5 deals with ordinary differential equations; Chapter 6 includes many concrete results for various fundamental partial differential equations. In Chapter 7, typical integral equations are presented with discretization methods. These chapters are applications of the general theories of Chapter 3 with the purpose of practical and numerical constructions of the solutions.
In Chapter 8, hot topics on reproducing kernels are presented; namely, norm inequalities, convolution inequalities, inversion of an arbitrary matrix, representations of inverse mappings, identifications of nonlinear systems, sampling theory, statistical learning theory and membership problems. Relationships among eigen-functions, initial value problems for linear partial differential equations, and reproducing kernels are also presented. Further, new fundamental results on generalized reproducing kernels, generalized delta functions, generalized reproducing kernel Hilbert spaces, andas well, a general integral transform theory are introduced.
In three Appendices, the deep theory of Akira Yamada discussing the equality problems in nonlinear norm inequalities, Yamada's unified and generalized inequalities for Opial's inequalities and the concrete and explicit integral representation of the implicit functions are presented.
Автор: Rassias Название: Mathematical Analysis, Approximation Theory and Their Applications ISBN: 3319312790 ISBN-13(EAN): 9783319312798 Издательство: Springer Рейтинг: Цена: 153720.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.
Автор: Vladimir K. Dobrev Название: Lie Theory and Its Applications in Physics ISBN: 9811026351 ISBN-13(EAN): 9789811026355 Издательство: Springer Рейтинг: Цена: 186330.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop 'Lie Theory and Its Applications in Physics', held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.
Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.<
This is a large interdisciplinary and interrelated field, and the present volume is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
Автор: Hislop Название: Introduction to Spectral Theory ISBN: 0387945016 ISBN-13(EAN): 9780387945019 Издательство: Springer Рейтинг: Цена: 158380.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This work aims to introduce students to active areas of research in mathematical physics in a rather direct way, thus minimizing the use of abstract mathematics. The book`s main features are geometric methods in spectral analysis, semi-classical analysis of resonance and other topics.
Автор: Christensen Название: An Introduction to Frames and Riesz Bases ISBN: 3319256114 ISBN-13(EAN): 9783319256115 Издательство: Springer Рейтинг: Цена: 74530.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field. Key features include:*Elementary introduction to frame theory in finite-dimensional spaces * Basic results presented in an accessible way for both pure and applied mathematicians * Extensive exercises make the work suitable as a textbook for use in graduate courses * Full proofs included in introductory chapters; only basic knowledge of functional analysis required * Explicit constructions of frames and dual pairs of frames, with applications and connections to time-frequency analysis, wavelets, and generalized shift-invariant systems* Discussion of frames on LCA groups and the concrete realizations in terms of Gabor systems on the elementary groups; connections to sampling theory * Selected research topics presented with recommendations for more advanced topics and further reading* Open problems to stimulate further research An Introduction to Frames and Riesz Bases will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference. Review of the first edition:'Ole Christensen’s An Introduction to Frames and Riesz Bases is a first-rate introduction to the field … . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research.' — Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005
Автор: Viola Название: An Introduction to Special Functions ISBN: 3319413449 ISBN-13(EAN): 9783319413440 Издательство: Springer Рейтинг: Цена: 53100.00 T Наличие на складе: Поставка под заказ. Описание: The subjects treated in this book have been especially chosen to represent a bridge connecting the content of a first course on the elementary theory of analytic functions with a rigorous treatment of some of the most important special functions: the Euler gamma function, the Gauss hypergeometric function, and the Kummer confluent hypergeometric function. Such special functions are indispensable tools in 'higher calculus' and are frequently encountered in almost all branches of pure and applied mathematics. The only knowledge assumed on the part of the reader is an understanding of basic concepts to the level of an elementary course covering the residue theorem, Cauchy's integral formula, the Taylor and Laurent series expansions, poles and essential singularities, branch points, etc. The book addresses the needs of advanced undergraduate and graduate students in mathematics or physics.
Автор: Sahoo Название: Introduction to Functional Equations ISBN: 143984111X ISBN-13(EAN): 9781439841112 Издательство: Taylor&Francis Рейтинг: Цена: 209270.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values.
In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections highlighting various developments of the main equations treated in that chapter. For advanced students, the book introduces functional equations in abstract domains like semigroups, groups, and Banach spaces.
Functional equations covered include:
Cauchy Functional Equations and Applications
The Jensen Functional Equation
Pexider's Functional Equation
Quadratic Functional Equation
D'Alembert Functional Equation
Trigonometric Functional Equations
Pompeiu Functional Equation
Hosszu Functional Equation
Davison Functional Equation
Abel Functional Equation
Mean Value Type Functional Equations
Functional Equations for Distance Measures
The innovation of solving functional equations lies in finding the right tricks for a particular equation. Accessible and rooted in current theory, methods, and research, this book sharpens mathematical competency and prepares students of mathematics and engineering for further work in advanced functional equations.
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