Structure of Fourier exponents of almost periodic functions and periodicity of almost periodic functions

Alexandr Fischer

Mathematica Bohemica (1996)

  • Volume: 121, Issue: 3, page 249-262
  • ISSN: 0862-7959

Abstract

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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 C P ( ) of continuous periodic functions is not densely distributed in the space A P ( ) .

How to cite

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Fischer, Alexandr. "Structure of Fourier exponents of almost periodic functions and periodicity of almost periodic functions." Mathematica Bohemica 121.3 (1996): 249-262. <http://eudml.org/doc/247983>.

@article{Fischer1996,
abstract = {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 $CP()$ of continuous periodic functions is not densely distributed in the space $AP()$.},
author = {Fischer, Alexandr},
journal = {Mathematica Bohemica},
keywords = {almost periodicity (Bohr); Fourier coefficient; Fourier exponent; Bochner transformation; almost periodicity (Bohr); Fourier coefficient; Fourier exponent; Bochner transformation},
language = {eng},
number = {3},
pages = {249-262},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Structure of Fourier exponents of almost periodic functions and periodicity of almost periodic functions},
url = {http://eudml.org/doc/247983},
volume = {121},
year = {1996},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 121
IS - 3
SP - 249
EP - 262
AB - 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 $CP()$ of continuous periodic functions is not densely distributed in the space $AP()$.
LA - eng
KW - almost periodicity (Bohr); Fourier coefficient; Fourier exponent; Bochner transformation; almost periodicity (Bohr); Fourier coefficient; Fourier exponent; Bochner transformation
UR - http://eudml.org/doc/247983
ER -

References

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  1. Amerio L., Prouse G., Almost periodic functions and functional equations, New York, Van Nostrand Reihold Company, 1971. (1971) Zbl0215.15701MR0275061
  2. Bohr H., Zur Theorie der fastperiodischen Funktionen, Acta Math. 45 (1925), 29-127, 46 (1925), 101-214, 47 (1926), 237-281. (1925) MR1555216
  3. Bochner S., 10.1007/BF01209156, Math. Ann. 96 (1927), 119-147. (1927) MR1512308DOI10.1007/BF01209156
  4. Bochner S., 10.1007/BF02547790, Acta Math. 61 (1933), 149-184. (1933) Zbl0007.11201MR1555374DOI10.1007/BF02547790
  5. Fink A.M., Almost periodic differential equations, Lecture Notes in Mathematics, New York, 1978. (1978) 
  6. Levitan B.M., Almost periodic functions, GIZTL, Moscow, 1953. (In Russian.) (1953) MR0060629
  7. Levitan B.M., Žikov V. V., Almost periodic functions and differential equations, IMU, Moscow, 1978. (In Russian.) (1978) MR0509035

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