Harmonic Analysis and Applications

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Sprache: Englisch

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Beschreibung

Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. Harmonic Analysis and Applications presents the analysis and synthesis of functions in terms of harmonics in a way that clearly demonstrates the vitality, power, elegance, usefulness of the subject.

Über den Autor

Benedetto, John J.

Inhaltsverzeichnis

Prologue I-Course I
Prologue II-Fourier Transforms, Fourier Series, and Discrete Fourier Transforms
Fourier Transforms
Definitions and Formal Calculations
Algebraic Properties of Fourier Transforms
Examples
Analytic Properties of Fourier Transforms
Convolution
Approximate Identities and Examples
Pointwise Inversion of the Fourier Transform
Partial Differential Equations
Gibbs Phenomenon
The L2(R) Theory Exercises
Measures and Distribution Theory
Approximate Identities Definition of Distributions
Differentiation of Distributions
The Fourier Transform of Distributions
Convolution of Distributions
Operational Calculus
Measure Theory
Definitions from Probability Theory
Wiener's Generalized Harmonic Analysis (GHA)
exp{it2}
Exercises
Fourier Series
Fourier Series - Definitions and Convergence
History of Fourier Series
Integration and Differentiation of Fourier Series
The L1(T) and L2(T) Theories A(T) and the Wiener Inversion Theorem Maximum Entropy and Spectral Estimation
Prediction and Spectral Estimation
Discrete Fourier Transform
Fast Fourier Transform
Periodization and Sampling
Exercises
Appendices
A. Real Analysis
B. Functional Analysis
C. Fourier Analysis Formulas
D. Contributors to Fourier Analysis
Notation
Bibliography
Index

Details

Erscheinungsjahr:	2019
Fachbereich:	Allgemeines
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Taschenbuch
ISBN-13:	9780367401276
ISBN-10:	0367401274
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Benedetto, John J.
Hersteller:	CRC Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	229 x 152 x 19 mm
Von/Mit:	John J. Benedetto
Erscheinungsdatum:	27.09.2019
Gewicht:	0,519 kg