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JOURNALS // Ufimskii Matematicheskii Zhurnal // Archive

Ufimsk. Mat. Zh., 2015 Volume 7, Issue 4, Pages 61–74 (Mi ufa301)

Various definitions of the spectrum of almost periodic functions

N. P. Girya, S. Yu. Favorov

V. N. Karazin Kharkiv National University, Kharkiv, Ukraine

Abstract: We consider various definitions of spectrum for almost periodic functions in a finite dimensional space for uniform, Stepanov, Weil, Besicovitch metrics. We prove that in these cases the classical definition of spectrum is equivalent to an analogue of definition of Beurling spectrum.

Keywords: almost periodic function, spectrum, Stepanov metric, Weil metric, Besicovitch metric, Beurling spectrum.

UDC: 517.518.6

MSC: 42А75, 30В50

Received: 25.08.2015


 English version:
Ufa Mathematical Journal, 2015, 7:4, 58–70

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© Steklov Math. Inst. of RAS, 2024