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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Hu, Z., Mingarelli, A.B. Bochner’s theorem and Stepanov almost periodic functions. Annali di Matematica 187, 719–736 (2008). https://doi.org/10.1007/s10231-008-0066-5
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DOI: https://doi.org/10.1007/s10231-008-0066-5
Keywords
- Bochner’s theorem
- Almost periodic
- Stepanov
- Favard
- Weyl
- Besicovitch
- Almost periodic functions
- Existence
- Minimizing norm
- Differential equations
- Systems