Boundary conditions for wave equation
	Factorization of its Green's operator (blue +, red -)

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.

List of Publications.