Geodesic
Construction of Mikusinski operational calculus based on the convolution algebra of distributions. The theorems and the beginning of use
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2013), pp. 56-68.

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

We consider the Mikusinski operational calculus based on the convolution algebra of distributions $D^\prime_+$ and $D^\prime_-$. We state and prove the basic theorems, and give examples of Mikusinski operational calculus using, which demonstrate its additional possibilities, such as extension of solutions to the domain of negative argument values, removing the growth limits of right-hand functions and obtaining the new methods for solving the nonhomogeneous equations with discontinuous right part.
Keywords: calculus of Mikusinski, space of distributions
Mots-clés : convolution of distributions, convolution algebra, Laplace transform. 
@article{VSGTU_2013_3_a4,
     author = {I. L. Kogan},
     title = {Construction of {Mikusinski} operational calculus based on the convolution algebra of distributions. {The} theorems and the beginning of use},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {56--68},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2013_3_a4/}
}
TY  - JOUR
AU  - I. L. Kogan
TI  - Construction of Mikusinski operational calculus based on the convolution algebra of distributions. The theorems and the beginning of use
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2013
SP  - 56
EP  - 68
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2013_3_a4/
LA  - ru
ID  - VSGTU_2013_3_a4
ER  - 
%0 Journal Article
%A I. L. Kogan
%T Construction of Mikusinski operational calculus based on the convolution algebra of distributions. The theorems and the beginning of use
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2013
%P 56-68
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2013_3_a4/
%G ru
%F VSGTU_2013_3_a4
I. L. Kogan. Construction of Mikusinski operational calculus based on the convolution algebra of distributions. The theorems and the beginning of use. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2013), pp. 56-68. http://geodesic.mathdoc.fr/item/VSGTU_2013_3_a4/

[1] I. L. Kogan, “Construction of Mikusinski operational calculus based on the convolution algebra of distributions. Basic provisions”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2012, no. 2(27), 44–52 | DOI | Zbl

[2] R. Courant, D. Hilbert, Methods of mathematical physics, v. 2, Partial differential equations, Interscience Publ., New York, 1962, 830 pp. ; R. Kurant, Uravneniya s chastnymi proizvodnymi, Mir, M., 1964, 830 pp. | Zbl | MR

[3] V. P. Maslov, Operator methods, Nauka, Moscow, 1973, 543 pp. | MR

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

[5] L. Schwartz, Methodes mathematiques pour les sciences physiques, Hermann, Paris, 1961, 392 pp. ; L. Shvarts, Matematicheskie metody dlya fizicheskikh nauk, Mir, M., 1965, 412 pp. | MR | Zbl | MR

[6] I. L. Kogan, “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