Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science

. Ed(s): Pesenson, Isaac; Thong Le Gia, Quoc; Mayeli, Azita; Mhaskar, Hrushikesh; Zhou, Ding Xuan

ISBN 10: 3319555553 / ISBN 13: 9783319555553

Published by Birkhauser Verlag AG, 2017

Editor(s): Pesenson, Isaac; Thong Le Gia, Quoc; Mayeli, Azita; Mhaskar, Hrushikesh; Zhou, Ding Xuan. Series: Applied and Numerical Harmonic Analysis. Num Pages: 443 pages, 26 black & white illustrations, biography. BIC Classification: PBKF; PBKS; PDE; UN. Category: (P) Professional & Vocational. Dimension: 235 x 155. . . 2017. 1st ed. 2017. Hardback. . . . . Seller Inventory # V9783319555553

Synopsis:

The second of a two volume set on novel methods in harmonic analysis, 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 harmonic analysis, 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 harmonic analysis to function spaces, differential equations, and data science, covering topics such as:

• The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems.
  
• Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets.
  
• Applications of harmonic analysis to data science and statistics
• Boundary-value problems for PDE's  including  the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.

From the Back Cover:

The second of a two volume set on novel methods in harmonic analysis, 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 harmonic analysis, 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 harmonic analysis to function spaces, differential equations, and data science, covering topics such as:

• The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems.
  
• Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets.
  
• Applications of harmonic analysis to data science and statistics
• Boundary-value problems for PDE's  including  the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.

Bibliographic Details

Title: Recent Applications of Harmonic Analysis to ...
Publisher: Birkhauser Verlag AG
Publication Date: 2017
Binding: Hardcover
Condition: New
Edition: 1st Edition