Bohr’s equivalence relation in the space of Besicovitch almost periodic functions
| Autor: | Teresa Vidal, Juan Matias Sepulcre |
|---|---|
| Přispěvatelé: | Universidad de Alicante. Departamento de Matemáticas, Curvas Alpha-Densas. Análisis y Geometría Local |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Almost periodic function
Análisis Matemático Almost periodic functions Algebra and Number Theory 010102 general mathematics 0102 computer and information sciences Function (mathematics) Space (mathematics) 01 natural sciences Fourier series Combinatorics Number theory 010201 computation theory & mathematics Besicovitch almost periodic functions Equivalence relation Exponential sums 0101 mathematics General Dirichlet series Bochner’s theorem Bochner's theorem Mathematics |
| Zdroj: | RUA. Repositorio Institucional de la Universidad de Alicante Universidad de Alicante (UA) |
| Popis: | Based on Bohr’s equivalence relation which was established for general Dirichlet series, in this paper we introduce a new equivalence relation on the space of almost periodic functions in the sense of Besicovitch, $$B(\mathbb {R},\mathbb {C})$$ , defined in terms of polynomial approximations. From this, we show that in an important subspace $$B^2(\mathbb {R},\mathbb {C})\subset B(\mathbb {R},\mathbb {C})$$ , where Parseval’s equality and the Riesz–Fischer theorem hold, its equivalence classes are sequentially compact and the family of translates of a function belonging to this subspace is dense in its own class. |
| Databáze: | OpenAIRE |
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