Uncertainty principles for Jacobi expansions

[摘要] In this paper an uncertainty principle for Jacobi expansions is derived, as a generalization of that for ultraspherical expansions by Rosler and Voit. Indeed a stronger inequality is proved, which is new even for Fourier cosine or ultraspherical expansions. A complex base of exponential type on the torus {z is an element of C: \z\ = 1} related to Jacobi polynomials is introduced, which are the eigenfunctions both of certain differential-difference operators of the first order and the second order. An uncertainty principle related to such exponential base is also proved. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-10-15

[关键词] uncertainty principle;Jacobi series;differential-difference