Fourier Series, Fourier Transform and Their Applications to Mathematical Physics
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Beschreibung
This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences. Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts.
The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing. The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations. The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory of partial differential equations.Complete with nearly 250 exercises throughout, this text is intended for graduate level students and researchers in the mathematical sciences and engineering.Each chapter is self-contained and can be read independently
Content grew from a series of half-semester courses given at University of Oulu
Contains material only previously published in scientific journals
Useful to both students and researchers who have applications in mathematical physics and engineering sciences
Each chapter is self-contained and can be read independently Content grew from a series of half-semester courses given at University of Oulu Contains material only previously published in scientific journals Useful to both students and researchers who have applications in mathematical physics and engineering sciences Includes supplementary material: sn.pub/extras Request lecturer material: sn.pub/lecturer-material
Autor*in
Valery Serov
Themen in »Fourier Series, Fourier Transform and Their Applications to Mathematical Physics«
Fourier Series Fourier Transforms Operator Theory Mathematical Phsycis Partial Differential Equations Freidrich's Extension Schrodinger Operator Scattering Theory Sobolev Spaces Born Approximation Elliptic Operator Fundamental Solution Reisz Theory
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“This book is an introduction to the modern theory of harmonic analysis and differential equations. … the book would be useful for graduate students as well as for researchers who look for applications in mathematical physics and engineering sciences.” (Sergeĭ Yu Tikhonov, Mathematical Reviews, February, 2019)
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