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.

This note
starts by introducing the basic concepts of function spaces and operators, both
from the continuous and discrete viewpoints. It introduces the Fourier and
Window Fourier Transform, the classical tools for function analysis in the
frequency domain.

This lecture note covers the following topics: Cesaro
summability and Abel summability of Fourier series, Mean square convergence of
Fourier series, Af continuous function with divergent Fourier series,
Applications of Fourier series Fourier transform on the real line and basic
properties, Solution of heat equation Fourier transform for functions in Lp,
Fourier transform of a tempered distribution Poisson summation formula,
uncertainty principle, Paley-Wiener theorem, Tauberian theorems, Spherical
harmonics and symmetry properties of Fourier transform, Multiple Fourier series
and Fourier transform on Rn.

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.

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.

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.

This note covers the following topics: The Fourier transform, Convolution, Fourier-Laplace Transform,
Structure Theorem for distributions and Partial Differential Equation.

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.

This note covers the following topics:
The Fourier transform, The semidiscrete Fourier transform, Interpolation and
sinc functions, The discrete Fourier transform, Vectors and multiple space
dimensions.

This note covers the following topics: Measures and measure spaces, Lebesgue's measure, Measurable functions,
Construction of integrals, Convergence of integrals, Lebesgue's dominated
convergence theorem, Comparison of measures, The Lebesgue spaces, Distributions
and Operations with distributions.

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

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.