Fourier Analysis And Hausdorff Dimension
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Fourier Analysis And Hausdorff Dimension
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Author : Pertti Mattila
language : en
Publisher: Cambridge University Press
Release Date : 2015-07-22
Fourier Analysis And Hausdorff Dimension written by Pertti Mattila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-22 with Mathematics categories.
Modern text examining the interplay between measure theory and Fourier analysis.
Harmonic Analysis And Fractal Analysis Over Local Fields And Applications
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Author : Su Weiyi
language : en
Publisher: World Scientific
Release Date : 2017-08-17
Harmonic Analysis And Fractal Analysis Over Local Fields And Applications written by Su Weiyi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-17 with Mathematics categories.
This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes/textbook or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research field.The book is self-contained, with wide scope and deep knowledge, taking modern mathematics (such as modern algebra, point set topology, functional analysis, distribution theory, and so on) as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. On the other hand, the author does his best to make those difficult concepts accessible to readers, illustrate clear comparison between harmonic analysis on Euclidean spaces and that on local fields, and at the same time provide motivations underlying the new concepts and techniques. Overall, it is a high quality, up to date and valuable book for interested readers.
Journal Of Fourier Analysis And Applications Special Issue
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Author : John J. Benedetto
language : en
Publisher: CRC Press
Release Date : 2020-03-10
Journal Of Fourier Analysis And Applications Special Issue written by John J. Benedetto and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-10 with Mathematics categories.
The Journal of Fourier Analysis and Applications is a journal of the mathematical sciences devoted to Fourier analysis and its applications. The subject of Fourier analysis has had a major impact on the development of mathematics, on the understanding of many engineering and scientific phenomena, and on the solution of some of the most important problems in mathematics and the sciences. At the end of June 1993, a large Conference in Harmonic Analysis was held at the University of Paris-Sud at Orsay to celebrate the prominent role played by Jean-Pierre Kahane and his numerous achievements in this field. The large variety of topics discussed in this meeting, ranging from classical Harmonic Analysis to Probability Theory, reflects the intense mathematical curiosity and the broad mathematical interest of Jean-Pierre Kahane. Indeed, all of them are connected to his work. The mornings were devoted to plenary addresses while up to four parallel sessions took place in the afternoons. Altogether, there were about eighty speakers. This wide range of subjects appears in these proceedings which include thirty six articles.
New Trends In Applied Harmonic Analysis
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Author : Akram Aldroubi
language : en
Publisher: Birkhäuser
Release Date : 2016-04-21
New Trends In Applied Harmonic Analysis written by Akram Aldroubi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-21 with Mathematics categories.
This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and cover both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.
Real Analysis
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Author : Elias M. Stein
language : en
Publisher: Princeton University Press
Release Date : 2009-11-28
Real Analysis written by Elias M. Stein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-28 with Mathematics categories.
Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels. Also available, the first two volumes in the Princeton Lectures in Analysis:
Operator Related Function Theory And Time Frequency Analysis
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Author : Karlheinz Gröchenig
language : en
Publisher: Springer
Release Date : 2014-11-25
Operator Related Function Theory And Time Frequency Analysis written by Karlheinz Gröchenig and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-25 with Mathematics categories.
This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo. The Symposium, and this book, are focused on two important fields of modern mathematical analysis: operator-related function theory and time-frequency analysis; and the profound interplay between them. Among the original contributions and overview lectures gathered here are a paper presenting multifractal analysis as a bridge between geometric measure theory and signal processing; local and global geometry of Prony systems and Fourier reconstruction of piecewise-smooth functions; Bernstein's problem on weighted polynomial approximation; singular distributions and symmetry of the spectrum; and many others. Offering a selection of the latest and most exciting results obtained by world-leading researchers, the book will benefit scientists working in Harmonic and Complex Analysis, Mathematical Physics and Signal Processing.
Lectures On Harmonic Analysis
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Author : Thomas H. Wolff
language : en
Publisher: American Mathematical Soc.
Release Date : 2003-09-17
Lectures On Harmonic Analysis written by Thomas H. Wolff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-17 with Mathematics categories.
This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform, convolution, the inversion theorem, the uncertainty principle and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in the later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for further reading and research. Technicalities are kept to a minimum, and simpler but more basic methods are often favored over the most recent methods. The clear style of the exposition and the quick progression from fundamentals to advanced topics ensures that both graduate students and research mathematicians will benefit from the book.
Wavelets Fractals And Fourier Transforms
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Author : M. Farge
language : en
Publisher:
Release Date : 1993
Wavelets Fractals And Fourier Transforms written by M. Farge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Proceedings of a conference in Cambridge, England, December 1990. Topics include wavelets, fractals, and order-two densities; iterated function systems and their applications; fractional Brownian motion and wavelets; wavelets and astronomical image analysis; the wavelet transform applied to flow around Antarctica; wavelet analysis of turbulence; solution of Burgers' equation by Fourier transform methods; the fractal dimension of oil-water interfaces in channel flows; and fractal aggregates in the atmosphere. No index. Annotation copyright by Book News, Inc., Portland, OR
New Trends In Applied Harmonic Analysis Volume 2
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Author : Akram Aldroubi
language : en
Publisher: Springer Nature
Release Date : 2019-11-26
New Trends In Applied Harmonic Analysis Volume 2 written by Akram Aldroubi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-26 with Mathematics categories.
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.
Fractals And Spectra
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Author : Hans Triebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-17
Fractals And Spectra written by Hans Triebel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-17 with Mathematics categories.
This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Most of the presented material is published here for the first time.