Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science: Novel Methods in Harmonic Analysis, Volume 2 (Applied and Numerical Harmonic Analysis) - Hardcover

Hardcover

ISBN 10: 3319555553 ISBN 13: 9783319555553

Publisher: Birkhäuser, 2017

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.

About this title

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.

Edition details

• Publisher: Birkhäuser
• Publication date: 2017
• Language: English
• ISBN 10: 3319555553
• ISBN 13: 9783319555553
• Binding: Hardcover
• Edition number: 1
• Number of pages: 524
• Editor: Pesenson Isaac, Le Gia Quoc Thong, Mayeli Azita, Mhaskar Hrushikesh, Zhou Ding-Xuan