The equivalence principle for almost periodic functions
作者： J. M. Sepulcre , T. Vidal , M. Righetti
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摘要: Given two arbitrary almost periodic functions, we prove that the existence of a common open vertical strip $V$, where both functions assume same set values on every substrip included in is necessary and sufficient condition for to have region periodicity be $^*$-equivalent. This represents an improvement previous results it settles problem Bohr's equivalence theorem not having converse.
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arxiv.org参考文章(10)
Constantin Corduneanu, Almost Periodic Oscillations and Waves ,(2009)
Abram Samoilovitch Besicovitch, Almost Periodic Functions ,(2014)
Tom M. Apostol, Modular Functions and Dirichlet Series in Number Theory ,(1976)
Norbert Wiener, A. S. Besicovitch, Almost periodic functions The Mathematical Gazette. ,vol. 16, pp. 275- ,(1932) , 10.2307/3605933
S. Bochner, A NEW APPROACH TO ALMOST PERIODICITY. Proceedings of the National Academy of Sciences of the United States of America. ,vol. 48, pp. 2039- 2043 ,(1962) , 10.1073/PNAS.48.12.2039
Mattia Righetti, On Bohr's equivalence theorem Journal of Mathematical Analysis and Applications. ,vol. 445, pp. 650- 654 ,(2017) , 10.1016/J.JMAA.2016.08.028
J.M. Sepulcre, T. Vidal, A generalization of Bohr's Equivalence Theorem arXiv: Complex Variables. ,(2017)
J.M. Sepulcre, T. Vidal, Bohr's equivalence relation in the space of Besicovitch almost periodic functions arXiv: Functional Analysis. ,(2017)
J.M. Sepulcre, T. Vidal, Sets of values of equivalent almost periodic functions arXiv: Complex Variables. ,(2018)
J. M. Sepulcre, T. Vidal, Almost Periodic Functions in terms of Bohr's Equivalence Relation Ramanujan Journal. ,vol. 46, pp. 245- 267 ,(2018) , 10.1007/S11139-017-9950-1