Symbolic Functional Analysis

Winter Semester 2005/2006

Markus.Rosenkranz@oeaw.ac.at



Semester: 5th
Time: Mondays 10:15 - 11:45
Location: HF9905
First Lecture: October 10

This lecture will give an overview of a highly exciting and brand new field of symbolic computation that could be baptized Symbolic Functional Analysis. Roughly speaking, it could be characterized as the algorithmic analysis of operator problems. As a whole, symbolic computation can be partitioned into three levels: Starting out with algebraic algorithms for numbers (traditional "computer algebra"), it proceeds to algebraizing functions (often called "computer algebra"), which is then continued by the symbolic treatment of operator problems ("symbolic functional analysis"). Of course, this hierachy is solely meant in terms of its fundamental types: Number, Number->Number and (Number->Number)->(Number->Number); this does not imply any grading in terms of difficulty.

After building up and clarifying the required algebraic tools, we will turn to studying various kinds of operator algebras. In this lecture, we will focus mainly on linear boundary value problems, including a complete solution algorithm for the ODE case.

The lecture notes for this course can be found here as a Mathematica notebook. Additionally, there is also a short summary of the chapter on Green's Polynomials in the form of Mathematica slides.