Regensburger, Georg and Rosenkranz, Markus and Middeke, Johannes (2009) A skew polynomial approach to integro-differential operators. In: Johnson, Jeremy R. and Park, Hyungju and Kaltofen, Erich, eds. Proceedings of the 2009 international symposium on Symbolic and algebraic computation. ACM, pp. 287-294. ISBN 978-1-60558-609-0.
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We construct the algebra of integro-differential operators over an ordinary integro-differential algebra directly in terms of normal forms. In the case of polynomial coefficients, we use skew polynomials for defining the integro-differential Weyl algebra as a natural extension of the classical Weyl algebra in one variable. Its normal forms, algebraic properties and its relation to the localization of differential operators are studied. Fixing the integration constant, we regain the integro-differential operators with polynomial coefficients.
|Item Type:||Book section|
|Uncontrolled keywords:||Integro-differential operators; skew polynomials; Weyl algebra; integro-differential algebra; Baxter algebra|
|Subjects:||Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics|
|Depositing User:||M.G. Rosenkranz|
|Date Deposited:||27 Jul 2012 15:43|
|Last Modified:||13 Aug 2012 10:24|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/29968 (The current URI for this page, for reference purposes)|
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