Bochner's theorem and Stepanov almost periodic functions

Annali di Matematica Pura ed Applicata

Volumn 187, Issue 4, 2008, Pages 719-736

  Hu, Zuosheng ^a   Mingarelli, Angelo B ^a  

^a CARLETON UNIVERSITY   (Canada)

Author keywords

Almost periodic; Almost periodic functions; Besicovitch; Bochner's theorem; Differential equations; Existence; Favard; Minimizing norm; Stepanov; Systems; Weyl

Indexed keywords

EID: 45849124979     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/s10231-008-0066-5     Document Type: Article

References (27)

1. Amerio, L.: Soluzioni quasi-periodiche, o limitate, di sistemi differenziali non lineari quasi-periodici, o limitati. Ann. Mat. Pura Appl. 39, 97-119 (1955)
2. Andres, J., Bersani, A.M.: Almost-periodicity problem as a fixed-point problem for evolution inclusions. Topol. Methods Nonlinear Anal. 18(2), 337-349 (2001)
3. Andres, J., Górniewicz, L.: Topological fixed point principles for boundary value problems. Kluwer, Dordrecht (2003)
4. Besicovitch, A.S.: Almost Periodic Functions. Dover, New York (1954)
5. Bochner, S.: A new approach to almost periodicity. Proc. Nat. Acad. Sci. U.S.A. 48, 2039-2043 (1962)
6. Bohr, H.: Almost Periodic Functions. Chelsea, New York (1951)
7. Coddington, E.A., Levinson, N.: Theory of Ordinary Differential Equations. McGraw-Hill, New York (1955)
8. Favard, J.: Leçons sur les Fonctions Presque-périodiques. Gauthier-Villars, (1933)
9. Fink, A.M.: Separated solutions of almost periodic differential equations. Mat-Fys. Madd. Danske Vid. Selsk 42, 87-92 (1989)
10. Haraux, A.: Asymptotic behavior for two-dimensional quasi-autonomous almost-periodic evolution equations. J. Diff. Equ. 66, 62-70 (1987)
11. Hu, Z.: Boundedness and Stepanov almost periodicity of solutions. Electron. J. Differ. Equ. 2005(35), 1-7 (2005)
12. Hu, Z., Mingarelli, A.B.: On a question in the theory of almost periodic differential equations. Proc. Am. Math. Soc. 127, 2665-2670 (1999)
13. Hu, Z., Mingarelli, A.B.: On a theorem of Favard. Proc. Am. Math. Soc. 132, 417-428 (2004)
14. Hu, Z., Mingarelli, A.B.: Favard's theorem for almost periodic processes in Banach space. Dyn. Syst. Appl. 14, 615-632 (2005)
15. Kaczorowski, J., Ramaré, O.: Almost periodicity of some error terms in prime number theory. Acta Arithmetica 106(3), 278-297 (2003)
16. Koizumi, S.: Hilbert transforms in the Stepanoff space. Proc. Jpn Acad. 38, 735-740 (1962)
17. Levitan, B.M., Zhikov, V.V.: Almost Periodic Functions and Differential Equations. Cambridge University Press, Cambridge (1982)
18. Miller, R.K.: On almost periodic differential equations. Bull. Am. Math. Soc. 70, 792-795 (1964)
19. Pandey, J.N.: The Hilbert transform of almost periodic functions and distributions. J. Comp. Anal. Appl. 6(3), 199-210 (2004)
20. Pankov, A.A.: Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations. Kluwer, Dordrecht (1990)
21. Seifert, G.: Stability conditions for separation and almost periodicity of solutions of differential equations. Contrib. Differ. Equ. 1 (1963), 483-487
22. (title changed to Journal of Differential Equations in vol. 2)
23. Seifert, G.: Stability conditions for existence of almost periodic solutions of almost periodic systems. J. Math. Anal. Appl. 10, 409-418 (1965)
24. Seifert, G.: Almost periodic solutions for almost periodic systems of ordinary differential equations. J. Differ. Equ. 2, 305-319 (1966)
25. Sell, G.R.: Nonautonomous differential equations and topological dynamics, I, II. Trans. Am. Math. Soc. 127 (1967), 241-262, and 263-283
26. Stepanov, W.: Über einige Verallgemeinerungen der fastperiodischen Funktionen. Math. Ann. 95, 473-498 (1926)
27. Ursell, H.D.: Parseval's theorem for almost-periodic functions. Proc. Lond. Math. Soc. 32(2), 402-440 (1931)