Support theorem for the fundamental solution to the Schrödinger equation on certain compact symmetric spaces |
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Authors: | Tomoyuki Kakehi |
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Institution: | Department of Mathematics, Faculty of Science, Okayama University, Okayama, 700-8530, Japan |
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Abstract: | In this paper we construct the fundamental solution to the Schödinger equation on a compact symmetric space with even root multiplicities using shift operators of Heckman and Opdam. Next, we prove that the support of the fundamental solution becomes a lower dimensional subset at a rational time whereas its support and its singular support coincide with the whole symmetric space at an irrational time. Moreover, we also show that generalized Gauss sums appear in the expression of the fundamental solution. |
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Keywords: | MSC: primary 33C67 43A90 secondary 43A85 |
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