Opérateurs Paraboliques Dans Le Calcul Opérationnel Des Distributions A Support Dans Rn+ n ≥ 1
Operational Calculi for the Euler Operator
2000 Mathematics Subject Classification: 44A40, 44A35A direct algebraic construction of a family of operational calculi for the Euler differential operator δ = t d/dt is proposed. It extends the Mikusiński's approach to the Heaviside operational calculus for the case when the classical Duhamel convolution is replaced by the convolution ...
Operational calculus and differential equations with infinitely smooth coefficients.
Operational Methods in the Environment of a Computer Algebra System
This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.The presented research is related to the operational calculus approach and its representative applications. Operational methods are considered, as well as their...
Operational Rules for a Mixed Operator of the Erdélyi-Kober Type
2000 Mathematics Subject Classification: 26A33 (main), 44A40, 44A35, 33E30, 45J05, 45D05In the paper, the machinery of the Mellin integral transform is applied to deduce and prove some operational relations for a general operator of the Erdélyi-Kober type. This integro-differential operator is a composition of a number of left-hand sided and right-hand sided Erdélyi-Kober derivatives and integrals. It is referred to in the paper as a mixed operator of the Erdélyi-Kober type. For special values of...
Operator
Operator Homomorhisms.
Periodic Boehmians.
Professor Jan Mikusiński-the 20th anniversary of his death
Quelques applications des éspaces de Silva et de leurs duals
Reduction of differential equations
Let (F,D) be a differential field with the subfield of constants C (c ∈ C iff Dc=0). We consider linear differential equations (1) , where , and the solution y is in F or in some extension E of F (E ⊇ F). There always exists a (minimal, unique) extension E of F, where Ly=0 has a full system of linearly independent (over C) solutions; it is called the Picard-Vessiot extension of F E = PV(F,Ly=0). The Galois group G(E|F) of an extension field E ⊇ F consists of all differential automorphisms of...
Remarks on the operational formulas for orthogonal polynomials
Series like Taylor's series.
The analysis of a class of exponential operation functions.
The Closure In The Space Of Mikusinski's Operators
The closure in the space of Mikusinski's operators.
The dual space of .
The existence and the uniqueness of distributional solutions of some systems of non-linear differential equations
The formal solution of Mikusiński operational differential equations with variable coefficients.
The Fourier integral for a certain class of distributions
The aim of this paper is to derive by elementary means a theorem on the representation of certain distributions in the form of a Fourier integral. The approach chosen was found suitable especially for students of post-graduate courses at technical universities, where it is in some situations necessary to restrict a little the extent of the mathematical theory when concentrating on a technical problem.