Mathematical-Analysis BooksFourier Analysis Books

# Topics in Fourier Analysis

## Topics in Fourier Analysis Topics in Fourier Analysis

This note is an overview of some basic notions is given, especially with an eye towards somewhat fractal examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids. Topics covered includes: Fourier series, Topological groups, Commutative groups, The Fourier transform, Banach algebras, p-Adic numbers, r-Adic integers and solenoids, Compactifications and Completeness.

Author(s): 182 Pages ##### Similar Books

Fourier Analysis and Related Topics

Aim of this note is to provide mathematical tools used in applications, and a certain theoretical background that would make other parts of mathematical analysis accessible to the student of physical science. Topics covered includes: Power series and trigonometric series, Fourier integrals, Pointwise convergence of Fourier series, Summability of Fourier series, Periodic distributions and Fourier series, Metric, normed and inner product spaces, Orthogonal expansions and Fourier series, Classical orthogonal systems and series, Eigenvalue problems related to differential equations, Fourier transformation of well-behaved functions, Fourier transformation of tempered distributions, General distributions and Laplace transforms. 341 Pages

Topics in Fourier Analysis

This note is an overview of some basic notions is given, especially with an eye towards somewhat fractal examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids. Topics covered includes: Fourier series, Topological groups, Commutative groups, The Fourier transform, Banach algebras, p-Adic numbers, r-Adic integers and solenoids, Compactifications and Completeness. 182 Pages

The nonlinear Fourier transform

The aim of this note is to give an introduction to nonlinear Fourier analysis from a harmonic analyst�s point of view. Topics covered includes: The nonlinear Fourier transform, The Dirac scattering transform, Matrix-valued functions on the disk, Proof of triple factorization, The SU(2) scattering transform, Rational Functions as Fourier Transform Data. 196 Pages

Lecture Notes in Fourier Analysis by Mohammad Asadzsdeh

This book is an introduction to Fourier analysis and related topics with applications in solving linear partial differential equations, integral equations as well as signal problems. 342 Pages

An Introduction to Fourier Analysis

This book explains the following topics: Infinite Sequences, Infinite Series and Improper Integrals, Fourier Series, The One-Dimensional Wave Equation, The Two-Dimensional Wave Equation, Introduction to the Fourier Transform, Applications of the Fourier Transform and Bessel�s Equation. 268 Pages

Lectures On Fourier Series

This note covers the following topics: Orthonormal Sets, Variations on the Theme, The Riemann-Lebesgue Lemma, The Dirichlet, Fourier and Fejer Kernels, Fourier Series of Continuous Functions, Fejers Theorem, Regularity, Pointwise Convergence, Termwise Integration, Termwise Differentiation. 52 Pages

Introduction to the theory of Fourier's series and integrals

This book describes the Theory of Infinite Series and Integrals, with special reference to Fourier's Series and Integrals. The first three chapters deals with limit and function, and both are founded upon the modern theory of real numbers. In Chapter IV the Definite Integral is treated from Kiemann's point of view, and special attention is given to the question of the convergence of infinite integrals. The theory of series whose terms are functions of a single variable, and the theory of integrals which contain an arbitrary parameter are discussed in Chapters, V and VI. 410 Pages

Fourier Transform Materials Analysis

This book focuses on the material analysis based on Fourier transform theory. The book chapters are related to FTIR and the other methods used for analyzing different types of materials. 260 Pages

Three Introductory Lectures on Fourier Analysis and Wavelets

This note covers the following topics: Vector Spaces with Inner Product, Fourier Series, Fourier Transform, Windowed Fourier Transform, Continuous wavelets, Discrete wavelets and the multiresolution structure, Continuous scaling functions with compact support. 59 Pages

Linear Filters, Sampling and FourierAnalysis

Goal of this note is to explain Mathematical foundations for digital image analysis, representation and transformation. Covered topics are: Sampling Continuous Signals, Linear Filters and Convolution, Fourier Analysis, Sampling and Aliasing. 44 Pages

FOURIER ANALYSIS Part I Yu. Safarov

This note covers the following topics: Series expansions, Definition of Fourier series, Sine and cosine expansions, Convergence of Fourier series, Mean square convergence, Complete orthonormal sets in L2, Fourier transform in L1(R1), Sine and cosine Fourier transforms, Schwartz space S(R1), Inverse Fourier transform, Pointwise inversion of the L1-Fourier transform. 40 Pages

An Introduction to Wavelets

This note covers the following topics: A Motivation for Wavelets, Wavelets and the Wavelet Transform, Comparision of the Fourier and Wavelet Transforms, Examples. 29 Pages

Fourier Series

Currently this section contains no detailed description for the page, will update this page soon. NA Pages

Fourier Series James S.Walker

This book covers the following topics: Historical Background, Definition of Fourier Series, Convergence of Fourier Series, Convergence in Norm, Summability of Fourier Series, Generalized Fourier Series and Discrete Fourier Series. 34 Pages

Fourier Series and Fourier Transforms

Currently this section contains no detailed description for the page, will update this page soon. NA Pages

The Fourier Transform and applications

Currently this section contains no detailed description for the page, will update this page soon. NA Pages

Advertisement