Almost periodic functions

✍ Scribed by A.S. Besicovitch

• Publisher: Dover
• Year: 1954
• Tongue: English
• Leaves: 192
• Category: Library

✦ Table of Contents

Page de titre
Preface
Introduction
Chapter I. UNIFORMLY ALMOST PERIODIC FUNCTIONS
1. Definition and elementary properties
2. Normality of u.a.p. functions
3. Mean values of u.a.p. functions and their Fourier series
4. Fundamental theorem of the theory of u.a.p. functions
5. Polynomial approximation to u.a.p. functions
6. Limit periodic functions
7. Base of u.a.p. functions. Connection of u.a.p. functions with limit periodic functions of several variables
8. Summation of Fourier series of u.a.p. functions by partial sums
9. Bochner-Fejér summation of u.a.p. functions
10. Some particular cases of Fourier series of u.a.p. functions
11. Arithmetical nature of translation numbers
12. u.a.p. functions of two variables
Chapter II. GENERALISATION OF ALMOST PERIODIC FUNCTIONS
Introduction
1. Auxiliary theorems and formulae
2. General closures and general almost periodicity
3. S a.p:functions
4. W a.p. functions
5. S^p a.p. and W^p a.p. functions (p>1)
6. B a.p. functions
7. B^r a.p. functions
8. Algorithm for polynomial approximation
9. Parseval equation and Riesc-Fischer theorem
Appendix. B^- a.p. FUNCTIONS
Chapter III. ANALYTIC ALMOST PERIODIC FUNCTIONS
1. Some auxiliary theorems in the theory of analytic functions
2. Definition of analytic almost periodic functions and their elementary properties
3. Dirichlet series
4. Behaviour of u.a.p. functions at σ=∞
5. On the behaviour of analytic functions outside the strip of uniform almost periodicity
6. On the behaviour of analytic functions on the boundary of the strip of uniform almost periodicity
Memoirs referred to in the text