ArticleOriginal scientific text
Title
Mean-periodic operational calculi
Authors 1, 2
Affiliations
- Institute of Mathematics, Bulgarian Academy of Sciences, Sofia 1090, Bulgaria
- Institute of Mathematics, Polish Academy of Sciences, Katowice Branch, Bankowa 14, 40-007 Katowice, Poland
Abstract
Elements of operational calculi for mean-periodic functions with respect to a given linear functional in the space of continuous functions are developed. Application for explicit determining of such solutions of linear ordinary differential equations with constant coefficients is given.
Bibliography
- J. Delsarte, Les fonctions moyenne-périodiques, J. Math. Pures Appl. (9) 14 (1935), 403-453.
- L. Schwartz, Théorie générale des fonctions moyenne-périodiques, Ann. of Math. (2) 48 (1947), 857-929.
- L. Ehrenpreis, Mean-periodic functions, varieties whose annihilator ideals are principal, Amer. J. Math. 77 (1955), 293-328 and 731-733.
- C. A. Berenstein and B. A. Taylor, Mean-periodic functions, Internat. J. Math. Math. Sci. 3 (1980), 199-235.
- J. Delsarte, Fonctions moyenne-périodiques sur un groupe abstrait, Ann. Soc. Sci. Bruxelles Sér. I Sci. Math. Phys. 57 (1937), No 1, 6-15; reprinted in his Oeuvres, Vol. I, 381-390.
- A. F. Leont'ev, Funkcii periodicheskie v srednem, Trudy letnei matematicheskoi shkoly, Konf. Teorii Funkcii, Kiev, 1966 (in Russian).
- J. Mikusiński, Operational Calculus, PWN-Pergamon Press, Vol. I, 1983.
- I. H. Dimovski, Convolutional Calculus, Kluwer, Dordrecht, 1990.
- A. F. Leont'ev, Exponential Series, Nauka, Moscow, 1976 (in Russian).
- S. I. Grozdev, A convolution approach to initial value problems for equations with right invertible operators, C. R. Acad. Bulgare Sci. 33(1980), 35-38.
- I. H. Dimovski, Nonlocal operational calculi, Proc. Steklov Inst. of Math. 203 (1994), 58-73 (in Russian).