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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…mehr

Produktbeschreibung
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, servesas 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.
Autorenporträt
Valery Serov is Professor of Mathematics at the University of Oulu. Professor Serov received his PhD in Applied Mathematics in 1979 from Lomonosov Moscow State University.  He has over 120 publications, including 3 textbooks published in Russian.
Rezensionen
"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." (Serge Yu Tikhonov, Mathematical Reviews, February, 2019)