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Keywords:
almost periodicity (Bohr); Fourier coefficient; Fourier exponent; Bochner transformation
almost periodicity (Bohr); Fourier coefficient; Fourier exponent; Bochner transformation
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 $AP(\X)$.
References:
[1] Amerio L., Prouse G.: Almost periodic functions and functional equations. New York, Van Nostrand Reihold Company, 1971. MR 0275061 | Zbl 0215.15701
[2] Bohr H.: Zur Theorie der fastperiodischen Funktionen. Acta Math. 45 (1925), 29-127, 46 (1925), 101-214, 47 (1926), 237-281. MR 1555216
[3] Bochner S.: Beiträge zur Theorie der fastperiodischen Funktionen. Math. Ann. 96 (1927), 119-147. DOI 10.1007/BF01209156 | MR 1512308
[4] Bochner S.: Abstrakte fastperiodische Funktionen. Acta Math. 61 (1933), 149-184. DOI 10.1007/BF02547790 | MR 1555374 | Zbl 0007.11201
[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 0060629
[7] Levitan B.M., Žikov V. V.: Almost periodic functions and differential equations. IMU, Moscow, 1978. (In Russian.) MR 0509035
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