### Gasper's identity and the Markov sequence problem

- Series
- Analysis Seminar
- Time
- Wednesday, February 10, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Jeff Geronimo – Georgia Tech

Gasper in his 1971 Annals of Math paper proved that the Jacobi polynomials
satisfy a product formula which generalized the product formula of
Gegenbauer for ultraspherical polynomials. Gasper proved this by showing that
certains sums of triple products of Jacobi polynomials are positive
generalizing results of Bochner who earlier proved a similar results for
ultraspherical polynomials. These results allow a convolution structure for
Jacobi polynomials. We will give a simple proof of Gasper's and Bochner's
results using a Markov operator found by Carlen, Carvahlo, and Loss in their study of the
Kac model in kinetic theory. This is joint work with Eric Carlen and Michael Loss.