Geodesic
Structure of Fourier exponents of almost periodic functions and periodicity of almost periodic functions
Mathematica Bohemica, Tome 121 (1996) no. 3, pp. 249-262

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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 $AP(\X)$.
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 $AP(\X)$.
DOI : 10.21136/MB.1996.125993
Classification : 42A32, 42A75
Keywords: almost periodicity (Bohr); Fourier coefficient; Fourier exponent; Bochner transformation 
Fischer, Alexandr. Structure of Fourier exponents of almost periodic functions and periodicity of almost periodic functions. Mathematica Bohemica, Tome 121 (1996) no. 3, pp. 249-262. doi: 10.21136/MB.1996.125993
@article{10_21136_MB_1996_125993,
     author = {Fischer, Alexandr},
     title = {Structure of {Fourier} exponents of almost periodic functions and periodicity of almost periodic functions},
     journal = {Mathematica Bohemica},
     pages = {249--262},
     year = {1996},
     volume = {121},
     number = {3},
     doi = {10.21136/MB.1996.125993},
     mrnumber = {1419878},
     zbl = {0863.42012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1996.125993/}
}
TY  - JOUR
AU  - Fischer, Alexandr
TI  - Structure of Fourier exponents of almost periodic functions and periodicity of almost periodic functions
JO  - Mathematica Bohemica
PY  - 1996
SP  - 249
EP  - 262
VL  - 121
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1996.125993/
DO  - 10.21136/MB.1996.125993
LA  - en
ID  - 10_21136_MB_1996_125993
ER  - 
%0 Journal Article
%A Fischer, Alexandr
%T Structure of Fourier exponents of almost periodic functions and periodicity of almost periodic functions
%J Mathematica Bohemica
%D 1996
%P 249-262
%V 121
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1996.125993/
%R 10.21136/MB.1996.125993
%G en
%F 10_21136_MB_1996_125993

[1] Amerio L., Prouse G.: Almost periodic functions and functional equations. New York, Van Nostrand Reihold Company, 1971. | MR | Zbl

[2] Bohr H.: Zur Theorie der fastperiodischen Funktionen. Acta Math. 45 (1925), 29-127, 46 (1925), 101-214, 47 (1926), 237-281. | MR

[3] Bochner S.: Beiträge zur Theorie der fastperiodischen Funktionen. Math. Ann. 96 (1927), 119-147. | DOI | MR

[4] Bochner S.: Abstrakte fastperiodische Funktionen. Acta Math. 61 (1933), 149-184. | DOI | MR | Zbl

[5] Fink A.M.: Almost periodic differential equations. Lecture Notes in Mathematics, New York, 1978.

[6] Levitan B.M.: Almost periodic functions. GIZTL, Moscow, 1953. (In Russian.) | MR

[7] Levitan B.M., Žikov V. V.: Almost periodic functions and differential equations. IMU, Moscow, 1978. (In Russian.) | MR

Cité par Sources :