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

Novel Methods in Harmonic Analysis, Volume 2

Isaac Pesenson, Quoc Thong Le Gia, Azita Mayeli, Hrushikesh Mhaskar, Ding-Xuan Zhou (Herausgeber)

Buch | Hardcover

XIV, 510 Seiten

2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-55555-3 (ISBN)

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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.

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, Frames, and Persistent Homology.- Multi-Penalty Regularization for Detecting Relevant Variables.- Stable Likelihood Computation for Gaussian Random Fields.

Erscheinungsdatum	07.09.2017
Reihe/Serie	Applied and Numerical Harmonic Analysis
Zusatzinfo	XIV, 510 p. 81 illus., 25 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	943 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Abstract harmonic analysis • Big Data • Complex analysis, complex variables • computational science and engineering • Databases • Data Mining • fourier analysis • Frames • Functional analysis & transforms • Functional analysis & transforms • Manifolds • Mathematics • mathematics and statistics • Maths for scientists • Numerical analysis • Sampling • Space Frequency • time-frequency analysis
ISBN-10	3-319-55555-3 / 3319555553
ISBN-13	978-3-319-55555-3 / 9783319555553
Zustand	Neuware