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The theory of distributions has numerous applications and is extensively used in mathematics, physics and engineering. There is however relatively little elementary expository literature on distribution theory. This book is intended as an introduction. Starting with the elementary theory of distributions, it proceeds to convolution products of distributions, Fourier and Laplace transforms, tempered distributions, summable distributions and applications. The theory is illustrated by several examples, mostly beginning with the case of the real line and then followed by examples in higher dimensions. This is a justified and practical approach, it helps the reader to become familiar with the subject. A moderate number of exercises are added.

Theory of distributions (Functional analysis) --- Convolutions (Mathematics) --- Fourier transformations. --- Laplace transformation. --- Transformation, Laplace --- Transformations, Fourier --- Transforms, Fourier --- Convolution transforms --- Transformations, Convolution --- Distribution (Functional analysis) --- Distributions, Theory of (Functional analysis) --- Functions, Generalized --- Generalized functions --- Calculus, Operational --- Differential equations --- Transformations (Mathematics) --- Fourier analysis --- Distribution (Probability theory) --- Functions --- Integrals --- Functional analysis --- Distribution Theory. --- Fourier Transform. --- Heat Equation. --- Laplace Transform. --- Tempered Distribution.

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This book is intended as an introduction to harmonic analysis and generalized Gelfand pairs. Starting with the elementary theory of Fourier series and Fourier integrals, the author proceeds to abstract harmonic analysis on locally compact abelian groups and Gelfand pairs. Finally a more advanced theory of generalized Gelfand pairs is developed. This book is aimed at advanced undergraduates or beginning graduate students. The scope of the book is limited, with the aim of enabling students to reach a level suitable for starting PhD research. The main prerequisites for the book are elementary real, complex and functional analysis. In the later chapters, familiarity with some more advanced functional analysis is assumed, in particular with the spectral theory of (unbounded) self-adjoint operators on a Hilbert space. From the contents Fourier series Fourier integrals Locally compact groups Haar measures Harmonic analysis on locally compact abelian groups Theory and examples of Gelfand pairs Theory and examples of generalized Gelfand pairs

Harmonic analysis. --- Fourier analysis. --- Analysis, Fourier --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Mathematical analysis --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Generalized Gelfand Pairs. --- Harmonic Analysis. --- Locally Compact Abelian Groups.

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Algebra

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