Differential and Integral Equations

A scale of almost periodic functions spaces

C. Corduneanut

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This paper contains a construction of a scale of almost periodic functions spaces, extending from the space of functions representable as sums of absolutely convergent series of complex exponentials, up to the space of Besicovitch, the largest for which the Parseval equality holds. Instead of using integral norms, that have been used in constructing almost periodic functions (Stepanov, Weyl, Besicovitch), one uses Minkowski's norms in the linear space of trigonometric polynomials, then completes the last space, endowed with Minkowski's norms with various indices between 1 and 2.

Article information

Differential Integral Equations, Volume 24, Number 1/2 (2011), 1-27.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Primary: 34C27: Almost and pseudo-almost periodic solutions


Corduneanut, C. A scale of almost periodic functions spaces. Differential Integral Equations 24 (2011), no. 1/2, 1--27. https://projecteuclid.org/euclid.die/1356019043

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