Fourier Series, Fourier Transforms, and Function Spaces: A Second Course in Analysis, Tim Hsu
Автор: Dyke Phil Название: Introduction to Laplace Transforms and Fourier Series ISBN: 144716394X ISBN-13(EAN): 9781447163947 Издательство: Springer Рейтинг: Цена: 35530.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This advanced undergraduate/graduate textbook provides an easy-to-read account of Fourier series, wavelets and Laplace transforms. It features many worked examples with all solutions provided.
Автор: Albert Boggess, Francis J. Narcowich Название: A First Course in Wavelets with Fourier Analysis, 2nd Edition ISBN: 0470431172 ISBN-13(EAN): 9780470431177 Издательство: Wiley Рейтинг: Цена: 113990.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Presenting the subject from the point of view of signal analysis, A First Course in Wavelets with Fourier Analysis, 2nd Edition provides a self-contained mathematical treatment of the subject that is accessible to a broad audience.
In the part on Fourier analysis, we discuss pointwise convergence results, summability methods and, of course, convergence in the quadratic mean of Fourier series. More advanced topics include a first discussion of Hardy spaces. We also spend some time handling general orthogonal series expansions, in particular, related to orthogonal polynomials. Then we switch to the Fourier integral, i.e. the Fourier transform in Schwartz space, as well as in some Lebesgue spaces or of measures.
Our treatment of ordinary differential equations starts with a discussion of some classical methods to obtain explicit integrals, followed by the existence theorems of Picard-Lindel f and Peano which are proved by fixed point arguments. Linear systems are treated in great detail and we start a first discussion on boundary value problems. In particular, we look at Sturm-Liouville problems and orthogonal expansions. We also handle the hypergeometric differential equations (using complex methods) and their relations to special functions in mathematical physics. Some qualitative aspects are treated too, e.g. stability results (Ljapunov functions), phase diagrams, or flows.
Our introduction to the calculus of variations includes a discussion of the Euler-Lagrange equations, the Legendre theory of necessary and sufficient conditions, and aspects of the Hamilton-Jacobi theory. Related first order partial differential equations are treated in more detail.
The text serves as a companion to lecture courses, and it is also suitable for self-study. The text is complemented by ca. 260 problems with detailed solutions.
Автор: Stein, Elias M. Shakarchi, Rami Название: Fourier analysis ISBN: 069111384X ISBN-13(EAN): 9780691113845 Издательство: Wiley Рейтинг: Цена: 97150.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Intended for students with a beginning knowledge of mathematical analysis, this first volume, in a three-part introduction to Fourier analysis, introduces the core areas of mathematical analysis while also illustrating the organic unity between them. It includes numerous examples and applications.
"This book is suitable as a textbook for an introductory undergraduate mathematics course on discrete Fourier and wavelet transforms for students with background in calculus and linear algebra. The particular strength of this book is its accessibility to students with no background in analysis. The exercises and computer explorations provide the reader with many opportunities for active learning. Studying from this text will also help students strengthen their background in linear algebra."
Mathematical Association of America
This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.
It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.
"This book is suitable as a textbook for an introductory undergraduate mathematics course on discrete Fourier and wavelet transforms for students with background in calculus and linear algebra. The particular strength of this book is its accessibility to students with no background in analysis. The exercises and computer explorations provide the reader with many opportunities for active learning. Studying from this text will also help students strengthen their background in linear algebra."
Mathematical Association of America
This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.
It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.
Автор: Lubos Pick, Alois Kufner, Oldrich John, Svatopluk Fucik Название: Function Spaces, 1 ISBN: 3110250411 ISBN-13(EAN): 9783110250411 Издательство: Walter de Gruyter Цена: 198290.00 T Наличие на складе: Нет в наличии. Описание: This is the first part of the second revised and extended edition of the well established book "Function Spaces" by Alois Kufner, Oldrich John, and Svatopluk Fucik. Like the first edition this monograph is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces in their research or lecture courses. This first volume is devoted to the study of function spaces, based on intrinsic properties of a function such as its size, continuity, smoothness, various forms of a control over the mean oscillation, and so on. The second volume will be dedicated to the study of function spaces of Sobolev type, in which the key notion is the weak derivative of a function of several variables.
Автор: Ferenc Weisz Название: Convergence and Summability of Fourier Transforms and Hardy Spaces ISBN: 3319568132 ISBN-13(EAN): 9783319568133 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces.
Автор: Ferenc Weisz Название: Martingale Hardy Spaces and their Applications in Fourier Analysis ISBN: 3540576231 ISBN-13(EAN): 9783540576235 Издательство: Springer Рейтинг: Цена: 37220.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This monograph deals with the theory of one-and two-parameter martingale Hardy spaces and their use in Fourier analysis. The atomic decomposition method is applied to both theories, and a new proof of Carleson`s convergence result, using martingale methods, is provided.
Автор: Huan-nan Shi Название: Schur-Convex Functions and Inequalities: Volume 1: Concepts, Properties, and Applications in Symmetric Function Inequalities ISBN: 3110606127 ISBN-13(EAN): 9783110606126 Издательство: Walter de Gruyter Рейтинг: Цена: 149940.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This two-volume work introduces the theory and applications of Schur-convex functions. The first volume introduces concepts and properties of Schur-convex functions, including Schur-geometrically convex functions, Schur-harmonically convex functions, Schur-power convex functions, etc. and also discusses applications of Schur-convex functions in symmetric function inequalities.
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.
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