Uncertainty principles for Jacobi expansions (Q1414221)

Motivated by Heisenberg-Weyl-type inequalities on the torus and the sphere \(S^2\) by E. Breitenberger, F. J. Narcovich, and J. D. Ward, M. Rösler and the reviewer derived a sharp Heisenberg-Weyl-type uncertainty principle for general ultraspherical expansions of function on an interval some years ago by using an additional reflection operator in the spirit of Dunkl operators. For certain parameters, this uncertainty principle may be regarded as an uncertainty principle for radial functions on unit spheres. In the paper under review, this result is extended to expansions of functions in terms of Jacobi polynomials. In particular, again the optimality of the constants is achieved by considering suitable heat kernels. From a geometric point of view, the result may be seen for certain parameters as an uncertainty principle for radial functions on projective spaces.