In the project Symbolic Functional Analysis, we aim at developing an algebraic theory and suitable algorithmic tools for operators that typically occur in analysis, e.g. differerential / integral / boundary operators. Their algebraic features are captured by identities describing interactions between basic operators. Modelling operators by noncommutative polynomials, Groebner basis methods can be applied.
A central topic is the symbolic treatment of boundary problems. The algebraic language of operators is used for specifying boundary problems (differential equations and boundary conditions) and solutions (Green's operators). Higher-order boundary problems are approached by factorization into lower-order subproblems with transformed boundary conditions; their Green's operators are then given by the corresponding composition.
- Symbolic solution of boundary problems for linear ordinary differential equations (LODEs).
- Factoring LODE boundary problems and Green's operators.
- Algebraic theory treating boundary problems for linear partial differential equations (LPDEs).
- Techniques and examples for factoring LPDE boundary problems and Green's operators (see figures).
- Constructing generalized solutions for nonlinear first-order ordinary differential equations.
- F1301: Noncommutative Groebner bases.
- F1302: Reasoning methods for Green's operators within Theorema.
- F1308: Analytic properties of boundary problems and Green's operators.
|Prof. Dr. Bruno Buchberger||9941 mail|
|Prof. Dr. Heinz W. Engl||9219 mail|
|Dr. Georg Regensburger||5230 mail|
|Msc. Loredana Tec||9983 mail|