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Book
Integration and Modern Analysis
Authors: ---
ISBN: 9780817646561 9780817643065 0817643060 9786613562098 0817646566 1280384174 Year: 2009 Publisher: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser,

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Abstract

A paean to twentieth century analysis, this modern text has several important themes and key features which set it apart from others on the subject. A major thread throughout is the unifying influence of the concept of absolute continuity on differentiation and integration. This leads to fundamental results such as the Dieudonné–Grothendieck theorem and other intricate developments dealing with weak convergence of measures. Key Features: * Fascinating historical commentary interwoven into the exposition; * Hundreds of problems from routine to challenging; * Broad mathematical perspectives and material, e.g., in harmonic analysis and probability theory, for independent study projects; * Two significant appendices on functional analysis and Fourier analysis. Key Topics: * In-depth development of measure theory and Lebesgue integration; * Comprehensive treatment of connection between differentiation and integration, as well as complete proofs of state-of-the-art results; * Classical real variables and introduction to the role of Cantor sets, later placed in the modern setting of self-similarity and fractals; * Evolution of the Riesz representation theorem to Radon measures and distribution theory; * Deep results in modern differentiation theory; * Systematic development of weak sequential convergence inspired by theorems of Vitali, Nikodym, and Hahn–Saks; * Thorough treatment of rearrangements and maximal functions; * The relation between surface measure and Hausforff measure; * Complete presentation of Besicovich coverings and differentiation of measures. Integration and Modern Analysis will serve advanced undergraduates and graduate students, as well as professional mathematicians. It may be used in the classroom or self-study.


Book
Excursions in Harmonic Analysis, Volume 3 : The February Fourier Talks at the Norbert Wiener Center
Authors: --- --- --- ---
ISBN: 9783319132303 3319132296 9783319132297 331913230X Year: 2015 Publisher: Cham : Springer International Publishing : Imprint: Birkhäuser,

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This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 – 2013. Containing cutting-edge results by an impressive array of mathematicians, engineers, and scientists in academia, industry, and government, it will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, physics, and engineering. Topics covered include ·        spectral analysis and correlation; ·        radar and communications: design, theory, and applications; ·        sparsity  ·        special topics in harmonic analysis. The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.


Book
Excursions in Harmonic Analysis, Volume 4 : The February Fourier Talks at the Norbert Wiener Center
Authors: --- --- --- ---
ISBN: 3319201875 3319201883 Year: 2015 Publisher: Cham : Springer International Publishing : Imprint: Birkhäuser,

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Abstract

This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 – 2013. Containing cutting-edge results by an impressive array of mathematicians, engineers, and scientists in academia, industry, and government, it will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, physics, and engineering. Topics covered include:   • Special Topics in Harmonic Analysis • Applications and Algorithms in the Physical Sciences • Gabor Theory • RADAR and Communications: Design, Theory, and Applications   The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.


Book
Excursions in Harmonic Analysis, Volume 5 : The February Fourier Talks at the Norbert Wiener Center
Authors: --- --- --- ---
ISBN: 3319547119 3319547100 Year: 2017 Publisher: Cham : Springer International Publishing : Imprint: Birkhäuser,

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This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 – 2016. Containing cutting-edge results by an impressive array of mathematicians, engineers, and scientists in academia, industry and government, it will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, physics, and engineering. Topics covered include: Theoretical harmonic analysis Image and signal processing Quantization Algorithms and representations The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.

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