Anders Hansen (Cambridge)
The Solvability Complexity Index and Approximations of Spectra of
Operators
Abstract:
In this talk we will discuss the following long standing and
fundamental problem: Given an operator on a separable Hilbert space (with
an orthonormal basis), can one compute/construct its spectrum from its
matrix elements. As we want such a construction to be useful in application
(i.e. implementable on a computer), we restrict ourselves to only allowing
the use of arithmetic operations and radicals of the matrix elements and
taking limits. We will give an affirmative answer to the question, and also
introduce a classification tool for the complexity of different
computational spectral problems, namely, the Solvability Complexity Index.