Generalized vector valued almost periodic and ergodic distributions

Journal of Mathematical Analysis and Applications

Volumn 314, Issue 1, 2006, Pages 363-381

  Basit, Bolis ^a   Günzler, Hans ^b  

^a MONASH UNIVERSITY   (Australia)

^b UNIVERSITY OF KIEL   (Germany)

Author keywords

Almost automorphic; Almost periodic; Difference differential systems; Distribution classes; Ergodic; Generalized almost periodic distributions; Mean classes; Primitive of distributions

Indexed keywords

EID: 28844504319     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.03.081     Document Type: Article

References (44)

1. L. Amerio G. Prouse Almost-Periodic Functions and Functional Equations 1971 Van Nostrand
2. W. Arendt C.J.K. Batty M. Hieber F. Neubrander Vector-Valued Laplace Transforms and Cauchy Problems Monogr. Math. vol. 96 2001 Birkhäuser Basel
3. B. Basit Generalization of two theorems of M.I. Kadets concerning the indefinite integral of abstract almost periodic functions Math. Notes 9 1971 181-186
4. B. Basit Some problems concerning different types of vector valued almost periodic functions Dissertationes Math. 338 1995 26
5. B. Basit H. Günzler Asymptotic behavior of solutions of systems of neutral and convolution equations J. Differential Equations 149 1998 115-142
6. B. Basit H. Günzler Generalized almost periodic and ergodic solutions of linear differential equations on the half line in Banach spaces J. Math. Anal. Appl. 282 2003 673-697
7. B. Basit H. Günzler Generalized Esclangon-Landau results and applications to linear difference-differential systems in Banach spaces J. Difference Equ. Appl. 10 2005 1005-1023
8. B. Basit, H. Günzler, Generalized vector valued almost periodic and ergodic distributions, Analysis paper 113, Monash Univ., Sept. 2002
9. B. Basit, H. Günzler, Harmonic analysis for generalized vector valued almost periodic and ergodic distributions, submitted for publication
10. B. Basit C. Zhang New almost periodic type functions and solutions of differential equations Canad. J. Math. 48 1996 1138-1153
11. S. Bochner Über gewisse Differential-und allgemeinere Gleichungen, deren Lösungen fastperiodisch sind, I-III Math. Ann. 102 1930 489-504
12. S. Bochner Remark on indefinite integrals of almost periodic functions J. London Math. Soc. 8 1933 250-254
13. P. Bohl Über eine Differentialgleichung der Störungstheorie J. Reine Angew. Math. 131 1906 268-321
14. H. Bohr Zur Theorie der fastperiodischen Funktionen Acta Math. 45 1925 29-127
15. H. Bohr E. Følner On some types of functional spaces Acta Math. 76 1944 31-155
16. H. Bohr O. Neugebauer Über lineare Differentialgleichungen mit konstanten Koeffizienten und fastperiodischer rechter Seite Nachr. Ges. Wiss. Göttingen Math.-Phys. Klasse 1926 8-22
17. G. Caracosta R. Doss Sur l'integrale d'une fonction presque périodique C. R. Acad. Sci. 246 1958 3207-3208
18. J. Diestel J.J. Uhl Vector Measures Math. Surveys vol. 15 1977 Amer. Math. Soc. Providence, RI
19. J. Dixmier P. Malliavin Factorizations de fonctions et de vecteurs indéfiniment différentiables Bull. Sci. Math. (2) 102 1978 305-330
20. R. Doss On bounded functions with almost periodic differences Proc. Amer. Math. Soc. 12 1961 488-489
21. R. Doss On the almost periodic solutions of a class of integro-differential-difference equations Ann. of Math. 81 1965 117-123
22. N. Dunford J.T. Schwartz Linear Operators, Parts I and II 1963 Interscience New York
23. W.F. Eberlein Abstract ergodic theorems and weak almost periodic functions Trans. Amer. Math. Soc. 67 1949 217-240
24. L. Ehrenpreis Solutions of some problems of division, IV Amer. J. Math. 82 1960 522-588
25. A.M. Fink Almost Periodic Differential Equations Lecture Notes in Math. 1974 Springer-Verlag
26. S. Goldberg P. Irwin Weakly almost periodic vector-valued functions Dissertationes Math. 157 1979 42
27. H. Günzler Integration of almost periodic functions Math. Z. 102 1967 253-287
28. H. Günzler Integration 1985 Bibliographisches Institut, Wissenschaftsverlag
29. E. Hille R.S. Phillips Functional Analysis and Semigroups 1957 Amer. Math. Soc. Colloq. Providence, RI
30. M.I. Kadets On the integration of almost periodic functions with values in Banach spaces Funct. Anal. Appl. 3 1969 228-230
31. B.M. Levitan Integration of almost periodic functions with values in Banach spaces Izv. Acad. Nauk Ser. Mat. 30 1966 1101-1110 (in Russian)
32. B.M. Levitan V.V. Zhikov Almost Periodic Functions and Differential Equations 1982 Cambridge Univ. Press
33. L.M. Loomis The spectral characterization of a class of almost periodic functions Ann. of Math. 72 1960 362-368
34. P. Milnes On vector-valued weakly almost periodic functions J. London Math. Soc. (2) 22 1980 467-472
35. L.A. Rubel W.A. Squires B.A. Taylor Irreducibility of certain entire functions with applications to harmonic analysis Ann. of Math. 108 1978 553-567
36. W.M. Ruess W.H. Summers Integration of asymptotically almost periodic functions and weak almost periodicity Dissertationes Math. 279 1989 35
37. W.M. Ruess W.H. Summers Ergodic theorems for semigroups of operators Proc. Amer. Math. Soc. 114 1992 423-432
38. L. Schwartz Distributions á valeures vectorielles Ann. Inst. Fourier 7 1957 1-139
39. L. Schwartz Théorie des distributions 1966 Hermann Paris
40. W. Stepanoff Über einige Verallgemeinerungen der fast periodischen Funktionen Math. Ann. 95 1926 473-498
41. K. Yosida Functional Analysis 1976 Springer-Verlag
42. S. Zaidman Almost-Periodic Functions in Abstract Spaces Res. Notes in Math. vol. 126 1985 Pitman Advanced Publishing Program Boston
43. C. Zhang Integration of vector-valued pseudo-almost periodic functions Proc. Amer. Math. Soc. 121 1994 167-174
44. C. Zhang Almost Periodic Type Functions and Ergodicity 2003 Science Press/Kluwer Academic