Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science : Novel Methods in Harmonic Analysis, Volume 2. 1st ed. 2017

種類:

電子ブック

責任表示:

edited by Isaac Pesenson, Quoc Thong Le Gia, Azita Mayeli, Hrushikesh Mhaskar, Ding-Xuan Zhou

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2017

著者名:

Pesenson, Isaac.

Le Gia, Quoc Thong.

Mayeli, Azita.

Mhaskar, Hrushikesh.

Zhou, Ding-Xuan.

SpringerLink (Online service)

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シリーズ名:

Applied and Numerical Harmonic Analysis ;

ISBN:

9783319555560 [3319555561]    

注記:

Introduction -- Characterization of Gevrey Regularity by a Class of FBI Transforms -- A Novel Mathematical Approach to the Theory of Translation Invariant Linear Systems -- Asymptotic Behaviour of the Fourier Transform of a Function of Bounded Variation -- Convergence and Regularization of Sampling Series -- Harmonic Analysis in Non-Euclidean Spaces: Theory and Application -- An Harmonic Analysis of Directed Graphs from Arithmetic Functions and Primes -- Sheaf and Duality Methods for Analyzing Multi-Model Systems -- On Boundary-Value Problems for a Partial Differential Equation with Caputo and Bessel Operator -- On the Solvability of the Zaremba Problem in Infinite Sectors and the Invertibility of Associated Singular Integral Operators -- On the Solution of the Oblique Derivative Problem by Constructive Runge-Walsh Concepts -- An Overview of Numerical Acceleration Techniques for Non-Linear Dimension Reduction -- Adaptive Density Estimation on the Circle by Nearly-Tight Frames -- Interactions between Kernels,
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 a

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