Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Serov, Valery
Titre(s) : Fourier series, Fourier transform and their applications to mathematical physics [Texte électronique] / Valery Serov
Publication : Cham : Springer, copyright 2017
Description matérielle : 1 online resource
Collection : Applied mathematical sciences ; v. 197
Lien à la collection : Applied mathematical sciences (Online)
Note(s) : Bibliogr. p. 529-531. Index
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 Schrdinger and magnetic Schrdinger 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
Sujet(s) : Fourier, Séries de
Indice(s) Dewey :
515.243 3 (23e éd.) = Analyse de Fourier et analyse harmonique
Identifiants, prix et caractéristiques : ISBN 9783319652627. - ISBN 3319652621. - ISBN 9783319652610 (erroné). - ISBN 3319652613
(erroné). - ISBN 9783319652634. - ISBN 331965263X. - ISBN 9783319879857. - ISBN 3319879855
Identifiant de la notice : ark:/12148/cb45779691s
Notice n° :
FRBNF45779691
(notice reprise d'un réservoir extérieur)
Table des matières : Part I: Fourier Series and the Discrete Fourier Transform ; Introduction ; Formulation
of Fourier Series ; Fourier Coefficients and their Properties ; Convolution and
Parseval Equality ; Fejer Means of Fourier Series: Uniqueness of the Fourier Series
; Riemann-Lebesgue Lemma ; Fourier Series of Square-Integrable Function: Riesz-Fischer
Theorem ; Besov and Holder Spaces ; Absolute Convergence: Bernstein and Peetre Theorems
; Dirichlet Kernel: Pointwise and Uniform Congergence ; Formulation of Discrete Fourier
Transform and its Properties ; Connection Between the Discrete Fourier Transform
and the Fourier Transform ; Some Applications of Discrete Fourier Transform ; Applications
to Solving Some Model Equations ; Part II: Fourier Transform and Distributions ;
Introduction ; Fourier Transform in Schwartz Space ; Fourier Transform inLp(Rn);1
p 2 ; Tempered Distributions ; Convolutions in S and S^1 ; Sobolev Spaces ; Homogeneous
Distributions ; Fundamental Solution of the Helmholtz Operator ; Estimates for Laplacian
and Hamiltonian ; Part III: Operator Theory and Integral Equations ; Introduction
; Inner Product Spaces and Hilbert Spaces ; Symmetric Operators in Hilbert Spaces
; J. von Neumann's Spectral Theorem ; Spectrum of Self-Adjoint Operators ; Quadratic
Forms: Freidrich's Extension ; Elliptic Differential Operators ; Spectral Function
; Schrodinger Operator ; Magnetic Schrodinger Operator ; Integral Operators with
Weak Singularities: Integral Equations of the First and Second Kind ; Volterra and
Singular Integral Equations ; Approximate Methods ; Part IV: Partial Differential
Equations ; Introduction ; Local Existence Theory ; The Laplace Operator ; The
Dirichlet and Neumman Problems ; Layer Potentials ; Elliptic Boundary Value Problems
; Direct Scattering Problem for Helmholtz Equation ; Some Inverse Scattering Problems
for the Schrodinger Operator ; The Heat Operator ; The Wave Operator.
