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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
Volume: 121
Issue: 3
Year: 1996
Pages: 249-262
Summary lang: English
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Category: math
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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
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Date available: 2009-09-24T21:19:08Z
Last updated: 2015-09-04
Stable URL: http://hdl.handle.net/10338.dmlcz/125993
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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, 10.1007/BF02395468
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
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