### Spectral properties of differential operators using orthogonal polynomials

The classical theorem by Bochner classies the second order dierential operators having polynomial eigenfunctions.

Generalising Bochner's approach we look at dierential operators for which there exists a suitable

basis of functions tridiagonalising the dierential operator. This gives the opportunity to describe the spectrum

of the dierential 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.

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