The applied and numerical harmonic analysis (ANHA) book series aims to provide the engineering, mathematical, and scienti?c communities with signi?cant devel- ments in harmonicanalysis, ranging from abstract harmonic...
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ISBN:
(数字)9780817647384
ISBN:
(纸本)9780817647377
The applied and numerical harmonic analysis (ANHA) book series aims to provide the engineering, mathematical, and scienti?c communities with signi?cant devel- ments in harmonicanalysis, ranging from abstract harmonicanalysis to basic app- cations. The title of the series re?ects the importance of applications and numerical implementation, but richness and relevance of applications and implementation - pend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbiotic evolution is axiomatic. harmonicanalysis is a wellspring of ideas and applicability that has ?ourished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship - tween harmonicanalysis and ?elds such as signal processing, partial differential equations (PDEs), and image processing is re?ected in our state-of-the-art ANHA series. Our vision of modern harmonicanalysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time-frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.
During his long and distinguished career, J. Rowland Higgins (1935-2020) made a substantial impact on many mathematical fields through his work on sampling theory, his deep knowledge of its history, and his service to...
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ISBN:
(数字)9783031411304
ISBN:
(纸本)9783031411298;9783031411328
During his long and distinguished career, J. Rowland Higgins (1935-2020) made a substantial impact on many mathematical fields through his work on sampling theory, his deep knowledge of its history, and his service to the community. This volume is a tribute to his work and legacy, featuring chapters written by distinguished mathematicians that explore cutting-edge research in sampling, approximation, signal analysis, and other related areas. An introductory chapter provides a biography of Higgins that explores his rich and unique life, along with a bibliography of his papers; a brief history of the SampTA meetings – of which he was a Founding Member – is also included. The remaining articles are grouped into four sections – classical sampling, theoretical extensions, frame theory, and applications of sampling theory – and explore Higgins’ contributions to these areas, as well as some of the latest developments.
The 7th International Workshop in analysis and its Applications (IWAA) was held at the University of Maine, June 1-6, 1997 and featured approxi mately 60 mathematicians. The principal theme of the workshop share...
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ISBN:
(数字)9781461222361
ISBN:
(纸本)9780817640583;9781461274674
The 7th International Workshop in analysis and its Applications (IWAA) was held at the University of Maine, June 1-6, 1997 and featured approxi mately 60 mathematicians. The principal theme of the workshop shares the title of this volume and the latter is a direct outgrowth of the workshop. IWAA was founded in 1984 by Professor Caslav V. Stanojevic. The first meeting was held in the resort complex Kupuri, Yugoslavia, June 1-10, 1986, with two pilot meetings preceding. The Organization Committee to gether with the Advisory Committee (R. P. Boas, R. R. Goldberg, J. P. Kahne) set forward the format and content of future meetings. A certain number of papers were presented that later appeared individually in such journals as the Proceedings of the AMS, Bulletin of the AMS, Mathematis chen Annalen, and the Journal of Mathematical analysis and its Applica tions. The second meeting took place June 1-10, 1987, at the same location. At the plenary session of this meeting it was decided that future meetings should have a principal theme. The theme for the third meeting (June 1- 10, 1989, Kupuri) was Karamata's Regular Variation. The principal theme for the fourth meeting (June 1-10, 1990, Kupuri) was Inner Product and Convexity Structures in analysis, Mathematical Physics, and Economics. The fifth meeting was to have had the theme, analysis and Foundations, organized in cooperation with Professor A. Blass (June 1-10, 1991, Kupuri).
The second of a two volume set on novel methods in harmonicanalysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discov...
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ISBN:
(数字)9783319555560
ISBN:
(纸本)9783319555553;9783319856933
The second of a two volume set on novel methods in harmonicanalysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science.;The chapters within cover an impressive range of ideas from both traditional and modern harmonicanalysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces.;Volume II is organized around the theme of recent applications of harmonicanalysis to function spaces, differential equations, and data science, covering topics such as:
This book gives an elementary introduction to a classical area of mathemat ics - approximation theory - in a way that naturally leads to the modern field of wavelets. The main thread throughout the book is the i...
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ISBN:
(数字)9780817644482
ISBN:
(纸本)9780817636005
This book gives an elementary introduction to a classical area of mathemat ics - approximation theory - in a way that naturally leads to the modern field of wavelets. The main thread throughout the book is the idea of ap proximating "complicated expressions" with "simpler expressions," and how this plays a decisive role in many areas of modern mathematics and its applications. One of the main goals of the presentation is to make it clear to the reader that mathematics is a subject in a state of continuous evolution. This fact is usually difficult to explain to students at or near their second year of uni versity. Often, teachers do not have adequate elementary material to give to students as motivation and encouragement for their further studies. The present book will be of use in this context because the exposition demon strates the dynamic nature of mathematics and how classical disciplines influence many areas of modern mathematics and applications. The book may lead readers toward more advanced literature, such as the other pub lications in the applied and numerical harmonic analysis series (ANHA), by introducing ideas presented in several of those books in an elementary context. The focus here is on ideas rather than on technical details, and the book is not primarily meant to be a textbook.
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