Geodesic
Construction of Mikusinski operational calculus based on the convolution algebra of distributions. Basic provisions
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 44-52.

Voir la notice de l'article provenant de la source Math-Net.Ru

The main provisions of the operational calculus based on the convolution algebra of distributions $D_{+}'$ and $D_{-}'$ that extends this method to the negative values of the argument are given. The relation between the proposed method and the classical operational calculus built on the Laplace transform is provided.
Keywords: calculus of Mikusinski, space of distributions
Mots-clés : convolution of distributions, convolution algebra, Laplace transform. 
@article{VSGTU_2012_2_a4,
     author = {I. L. Kogan},
     title = {Construction of {Mikusinski} operational calculus based on the convolution algebra of distributions. {Basic} provisions},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {44--52},
     publisher = {mathdoc},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a4/}
}
TY  - JOUR
AU  - I. L. Kogan
TI  - Construction of Mikusinski operational calculus based on the convolution algebra of distributions. Basic provisions
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2012
SP  - 44
EP  - 52
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a4/
LA  - ru
ID  - VSGTU_2012_2_a4
ER  - 
%0 Journal Article
%A I. L. Kogan
%T Construction of Mikusinski operational calculus based on the convolution algebra of distributions. Basic provisions
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2012
%P 44-52
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a4/
%G ru
%F VSGTU_2012_2_a4
I. L. Kogan. Construction of Mikusinski operational calculus based on the convolution algebra of distributions. Basic provisions. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 44-52. http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a4/

[1] Mikusinski J., Operational calculus, Pergamon Press, New York, 1959, 495 pp. ; Mikusinskii Ya., Operatornoe ischislenie, Inostr. lit., M., 1956, 366 pp. | MR | Zbl | MR

[2] Schwartz L., Méthodes mathématiques pour les sciences physiques, Hermann, Paris, 1961, 39 pp. ; Shvarts L., Matematicheskie metody dlya fizicheskikh nauk, Mir, M., 1965, 412 pp. | MR | Zbl | MR

[3] Vladimirov V. S., Generalized functions in mathematical physics, Nauka, Moscow, 1979, 319 pp. | MR

[4] Kogan I. L., “Method of Duhamel integral for ordinary differential equations with constant coefficients in respect to the theory of distributions”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2010, no. 1(20), 37–45 | DOI

[5] Gel'fand I. M., Shilov G. E., Generalized functions, v. 1, Properties and operations, Academic Press, New York, 1964, 423 pp.

[6] Lavrent'ev M. A., Shabat B. V., Methods of the theory of functions in a complex variable, Nauka, Moscow, 1987, 688 pp. | MR | Zbl