The Paley-Wiener Theorem and the Local Huygens' Principle for Compact Symmetric Spaces

Details The Paley-Wiener Theorem and the Local Huygens' Principle for Compact Symmetric Spaces The Paley-Wiener Theorem and the Local Huygens' Principle for Compact Symmetric Spaces

2004-11-17

arxiv.org/abs/math/0411383v1

Mathematics

Analysis of PDEs

26 pages, 1 figure

Scientific paper

We prove a Paley-Wiener Theorem for a class of symmetric spaces of the compact type, in which all root multiplicities are even. This theorem characterizes functions of small support in terms of holomorphic extendability and exponential type of their (discrete) Fourier transforms. We also provide three independent new proofs of the strong Huygens' principle for a suitable constant shift of the wave equation on odd-dimensional spaces from our class.

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