| Title:
|
Structure of Fourier exponents of almost periodic functions and periodicity of almost periodic functions (English) |
| Author:
|
Fischer, Alexandr |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
121 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
249-262 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with almost periodic functions which are limits of sequences of continuous periodic functions, and determines the structure of their Fourier exponents and their ranges. It is shown that the class $CP(\X)$ of continuous periodic functions is not densely distributed in the space $AP(\X)$. (English) |
| Keyword:
|
almost periodicity (Bohr) |
| Keyword:
|
Fourier coefficient |
| Keyword:
|
Fourier exponent |
| Keyword:
|
Bochner transformation |
| MSC:
|
42A32 |
| MSC:
|
42A75 |
| idZBL:
|
Zbl 0863.42012 |
| idMR:
|
MR1419878 |
| DOI:
|
10.21136/MB.1996.125993 |
| . |
| Date available:
|
2009-09-24T21:19:08Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125993 |
| . |
| Reference:
|
[1] Amerio L., Prouse G.: Almost periodic functions and functional equations.New York, Van Nostrand Reihold Company, 1971. Zbl 0215.15701, MR 0275061 |
| Reference:
|
[2] Bohr H.: Zur Theorie der fastperiodischen Funktionen.Acta Math. 45 (1925), 29-127, 46 (1925), 101-214, 47 (1926), 237-281. MR 1555216 |
| Reference:
|
[3] Bochner S.: Beiträge zur Theorie der fastperiodischen Funktionen.Math. Ann. 96 (1927), 119-147. MR 1512308, 10.1007/BF01209156 |
| Reference:
|
[4] Bochner S.: Abstrakte fastperiodische Funktionen.Acta Math. 61 (1933), 149-184. Zbl 0007.11201, MR 1555374, 10.1007/BF02547790 |
| Reference:
|
[5] Fink A.M.: Almost periodic differential equations.Lecture Notes in Mathematics, New York, 1978. |
| Reference:
|
[6] Levitan B.M.: Almost periodic functions.GIZTL, Moscow, 1953. (In Russian.) MR 0060629 |
| Reference:
|
[7] Levitan B.M., Žikov V. V.: Almost periodic functions and differential equations.IMU, Moscow, 1978. (In Russian.) MR 0509035 |
| . |
