Bochner’s theorem and Stepanov almost periodic functions |
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Authors: | Zuosheng Hu Angelo B Mingarelli |
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Institution: | (1) School of Mathematics and Statistics, Carleton University, Ottawa, K1S 5B6, Canada |
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Abstract: | Motivated by a renewed interest in generalizations of classical almost periodicity (originally due to Harald Bohr), we develop
a theorem of Bochner within the framework of almost periodic functions in the sense of Stepanov. As a result we establish
some conditions that guarantee the existence of Stepanov almost periodic solutions to differential equations with Stepanov
almost periodic coefficients. Finally, we extend a now classic theorem of Favard originally stated for classical almost periodic
functions to the Stepanov almost periodic case.
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Keywords: | Bochner’ s theorem Almost periodic Stepanov Favard Weyl Besicovitch Almost periodic functions Existence Minimizing norm Differential equations Systems |
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