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Bivariate delta-evolution equations and convolution polynomials: Computing polynomial expansions of solutions

Morón, Manuel A. and Luzón, Ana (2011) Bivariate delta-evolution equations and convolution polynomials: Computing polynomial expansions of solutions. Applied Mathematics and Computation, 218 (4). pp. 1417-1435. ISSN 0096-3003

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Abstract

This paper describes an application of Rota and collaborator's ideas, about the foundation on combinatorial theory, to the computing of solutions of some linear functional partial differential equations. We give a dynamical interpretation of the convolution families of polynomials. Concretely, we interpret them as entries in the matrix representation of the exponentials of certain contractive linear operators in the ring of formal power series. This is the starting point to get symbolic solutions for some functional-partial differential equations. We introduce the bivariate convolution product of convolution families to obtain symbolic solutions for natural extensions of functional-evolution equations related to delta-operators. We put some examples to show how these symbolic methods allow us to get closed formulas for solutions of genuine partial differential equations. We create an adequate framework to base theoretically some of the performed constructions and to get some existence and uniqueness results.

Item Type:Article
Uncontrolled Keywords:Riordan arrays; matrices; Ultrametric; Convolution family; Delta-operator; Riordan group; Delta-evolution equation; Bivariate convolution
Subjects:Sciences > Mathematics > Algebra
ID Code:14894
Deposited On:19 Apr 2012 09:10
Last Modified:06 Feb 2014 10:11

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