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Uncertainty principles for Jacobi expansions

✍ Scribed by Zhongkai Li; Limin Liu

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
201 KB
Volume
286
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper an uncertainty principle for Jacobi expansions is derived, as a generalization of that for ultraspherical expansions by Râsler 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 ∈ 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.

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