Uncertainty principles for Jacobi expansions |
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Authors: | Zhongkai Li Limin Liu |
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Affiliation: | Department of Mathematics, Capital Normal University, Beijing 100037, China |
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Abstract: | In this paper an uncertainty principle for Jacobi expansions is derived, as a generalization of that for ultraspherical expansions by Rösler 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 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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Keywords: | Uncertainty principle Jacobi series Differential-difference operator |
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