Spectral properties of differential operators using orthogonal polynomials
The classical theorem by Bochner classi es the second order di erential operators having polynomial eigenfunctions.
Generalising Bochner's approach we look at di erential operators for which there exists a suitable
basis of functions tridiagonalising the di erential operator. This gives the opportunity to describe the spectrum
of the di erential operators involved. We illustrate the approach by several examples, and we discuss
generalisations to other types of operators. A particular well-known example is the Schrodinger with the
Morse potential studied by chemists. Other examples to be discussed are the Jacobi function transform
and the Whittaker transform as well as some q-analogues.
** This is a joint work with: M. Ismail.
