Compendium of New Techniques in Harmonic Analysis PDF Download
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Author: Moulay Tahar Lamchich
Publisher: BoD – Books on Demand
ISBN: 1789236363
Category : Technology & Engineering
Languages : en
Pages : 198
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Book Description
Harmonic analysis is a diverse field including such branches as signal processing, medical imaging, power electrical systems, wireless telecommunications, etc. This book is primarily written with the objective of providing recent developments and new techniques in harmonic analysis. In the recent years, a number of methods of quality control of signals under different perturbations, and especially the harmonics, have emerged. Some of these techniques are described in this book. This book is the result of contributions from many researchers and is a collection of eight research works, which are focused around the harmonic analysis theme but with different applications. The topics mainly concern the areas of medical imaging, biopotential systems, renewable energy conversion systems, wireless telecommunications, power converters, as well as the different techniques for estimating, analyzing, reducing, and eliminating harmonics.
Author: Moulay Tahar Lamchich
Publisher: BoD – Books on Demand
ISBN: 1789236363
Category : Technology & Engineering
Languages : en
Pages : 198
Get Book Here
Book Description
Harmonic analysis is a diverse field including such branches as signal processing, medical imaging, power electrical systems, wireless telecommunications, etc. This book is primarily written with the objective of providing recent developments and new techniques in harmonic analysis. In the recent years, a number of methods of quality control of signals under different perturbations, and especially the harmonics, have emerged. Some of these techniques are described in this book. This book is the result of contributions from many researchers and is a collection of eight research works, which are focused around the harmonic analysis theme but with different applications. The topics mainly concern the areas of medical imaging, biopotential systems, renewable energy conversion systems, wireless telecommunications, power converters, as well as the different techniques for estimating, analyzing, reducing, and eliminating harmonics.
Author: Carlos E. Kenig
Publisher: American Mathematical Soc.
ISBN: 0821803093
Category : Mathematics
Languages : en
Pages : 162
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Book Description
In recent years, there has been a great deal of activity in the study of boundary value problems with minimal smoothness assumptions on the coefficients or on the boundary of the domain in question. These problems are of interest both because of their theoretical importance and the implications for applications, and they have turned out to have profound and fascinating connections with many areas of analysis. Techniques from harmonic analysis have proved to be extremely useful in these studies, both as concrete tools in establishing theorems and as models which suggest what kind of result might be true. Kenig describes these developments and connections for the study of classical boundary value problems on Lipschitz domains and for the corresponding problems for second order elliptic equations in divergence form. He also points out many interesting problems in this area which remain open.
Author: Maurice A. de Gosson
Publisher: Springer Science & Business Media
ISBN: 3764399929
Category : Mathematics
Languages : en
Pages : 351
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Book Description
The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space where the main role is played by “Bopp operators” (also called “Landau operators” in the literature) is introduced and studied. This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references.
Author: Baoxiang Wang
Publisher: World Scientific
ISBN: 9814458392
Category : Mathematics
Languages : en
Pages : 298
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Book Description
This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods.This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.
Author: Akram Aldroubi
Publisher: Springer Nature
ISBN: 3030323536
Category : Mathematics
Languages : en
Pages : 335
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Book Description
This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.
Author: Alberto Torchinsky
Publisher: Elsevier
ISBN: 1483268888
Category : Mathematics
Languages : en
Pages : 475
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Book Description
Real-Variable Methods in Harmonic Analysis deals with the unity of several areas in harmonic analysis, with emphasis on real-variable methods. Active areas of research in this field are discussed, from the Calderón-Zygmund theory of singular integral operators to the Muckenhoupt theory of Ap weights and the Burkholder-Gundy theory of good ? inequalities. The Calderón theory of commutators is also considered. Comprised of 17 chapters, this volume begins with an introduction to the pointwise convergence of Fourier series of functions, followed by an analysis of Cesàro summability. The discussion then turns to norm convergence; the basic working principles of harmonic analysis, centered around the Calderón-Zygmund decomposition of locally integrable functions; and fractional integration. Subsequent chapters deal with harmonic and subharmonic functions; oscillation of functions; the Muckenhoupt theory of Ap weights; and elliptic equations in divergence form. The book also explores the essentials of the Calderón-Zygmund theory of singular integral operators; the good ? inequalities of Burkholder-Gundy; the Fefferman-Stein theory of Hardy spaces of several real variables; Carleson measures; and Cauchy integrals on Lipschitz curves. The final chapter presents the solution to the Dirichlet and Neumann problems on C1-domains by means of the layer potential methods. This monograph is intended for graduate students with varied backgrounds and interests, ranging from operator theory to partial differential equations.
Author: Jos Arrillaga
Publisher: John Wiley & Sons
ISBN: 9780471975489
Category : Technology & Engineering
Languages : en
Pages : 390
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Book Description
Die Sicherung einer Stromversorgung in hoher Qualität ist heute von überragender Bedeutung. Die Anwesenheit von Verzerrungen führt zu verschiedensten Problemen. Dieses Buch präsentiert neue Methoden zur Zeit- und Frequenzdomänenmodellierung, Fourieranalyse und Identifikation von Erd- und Leiterimpedanzen von Stromversorgungssystemen.
Author: Vasily Vasyunin
Publisher: Cambridge University Press
ISBN: 1108486894
Category : Mathematics
Languages : en
Pages : 465
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Book Description
A comprehensive reference on the Bellman function method and its applications to various topics in probability and harmonic analysis.
Author: Alexey N. Karapetyants
Publisher: Springer Nature
ISBN: 3030774937
Category : Mathematics
Languages : en
Pages : 585
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Book Description
This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.
Author: Anton Deitmar
Publisher: Springer Science & Business Media
ISBN: 147573834X
Category : Mathematics
Languages : en
Pages : 154
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Book Description
This book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The final goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.
