عنوان

Almost periodic functions

(Number (ISBN

082840027X

(Number (ISBN

9780828400275

Number

b555676

Title Proper

Almost periodic functions

General Material Designation

[Book]

First Statement of Responsibility

by Harald Bohr. Text transl. by Harvey Cohn.

Place of Publication, Distribution, etc.

New York, NY

Name of Publisher, Distributor, etc.

Chelsea Publ.

Date of Publication, Distribution, etc.

[1999?]

Specific Material Designation and Extent of Item

113 Seiten

Text of Note

Introduction Purely periodic functions and their Fourier series: General orthogonal systems; Fourier constants with respect to a normal orthogonal system. Their minimal property. Bessel's formula and Bessel's inequality; Fourier series of periodic functions; Operations with Fourier series; Two fundamental theorems. The uniqueness theorem and Parseval's equation; Lebesgue's proof of the uniqueness theorem; The multiplication theorem; Summability of the Fourier series. Fejer's theorem; Weierstrass' theorem; Two remarks The theory of almost periodic functions: The main problem of the theory; Translation numbers; Definition of almost periodicity; Two simple properties of almost periodic functions; The invariance of almost periodicity under simple operations of calculation; The mean value theorem; The concept of the Fourier series of an almost periodic function. Derivation of Parseval's equation; Calculations with Fourier series; The uniqueness theorem. Its equivalence with Parseval's equation; The multiplication theorem; Introductory remarks to the proof of the two fundamental theorems; Preliminaries for the proof of the uniqueness theorem; Proof of the uniqueness theorem; The fundamental theorem; An important example Appendix I: Generalizations of almost periodic functions Appendix II: Almost periodic functions of a complex variable Bibliography.

Parallel Title

Fastperiodische Funktionen.

Class number

Book number

by Harald Bohr. Text transl. by Harvey Cohn.

Harald Bohr

Electronic name

[Book]

Y