Algebraic and Algorithmic Aspects of Differential and Integral Operators

1. Front Matter

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2. Constructions of Free Commutative Integro-Differential Algebras

   • Xing Gao, Li Guo

   Pages 1-22

3. Basic Module Theory over Non-commutative Rings with Computational Aspects of Operator Algebras

   • José Gómez-Torrecillas

   Pages 23-82

4. Operational Calculi for Nonlocal Cauchy Problems in Resonance Cases

   • Ivan Dimovski, Margarita Spiridonova

   Pages 83-95

5. Intertwining Laplace Transformations of Linear Partial Differential Equations

   • Elena I. Ganzha

   Pages 96-115

6. Composing and Factoring Generalized Green’s Operators and Ordinary Boundary Problems

   • Anja Korporal, Georg Regensburger

   Pages 116-134

7. Relativistic Coulomb Integrals and Zeilberger’s Holonomic Systems Approach II

   • Christoph Koutschan, Peter Paule, Sergei K. Suslov

   Pages 135-145

8. Multivariate Dimension Polynomials of Inversive Difference Field Extensions

   • Alexander Levin

   Pages 146-163

9. Differential (Monoid) Algebra and More

   • Laurent Poinsot

   Pages 164-189

10. Exact Solution of Local and Nonlocal BVPs for the Laplace Equation in a Rectangle

    • Yulian Tsankov

    Pages 190-200

11. Back Matter

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This book constitutes the proceedings of the 5th International Meeting on Algebraic and Algorithmic Aspects of Differential and Integral Operators, AADIOS 2012, held at the Applications of Computer Algebra Conference in Sofia, Bulgaria, on June 25-28, 2012. The total of 9 papers presented in this volume consists of 2 invited papers and 7 regular papers which were carefully reviewed and selected from 13 submissions. The topics of interest are: symbolic computation for operator algebras, factorization of differential/integral operators, linear boundary problems and green's operators, initial value problems for differential equations, symbolic integration and differential galois theory, symbolic operator calculi, algorithmic D-module theory, rota-baxter algebra, differential algebra, as well as discrete analogs and software aspects of the above.

• free algebra
• gröbner basis
• operational calculus
• operator algebra
• reduction
• algorithm analysis and problem complexity
• partial differential equations

• XLIM, DMI, University of Limoges, Limoges cedex, France

  Moulay Barkatou, Thomas Cluzeau

• Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria

  Georg Regensburger

• SMAS, University of Kent, Canterbury, UK

  Markus Rosenkranz

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