Support theorem for the fundamental solution to the Schrödinger equation on certain compact symmetric spaces

Tomoyuki Kakehi

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)2739-2763
Number of pages25
JournalAdvances in Mathematics
Volume226
Issue number3
DOIs
Publication statusPublished - Feb 15 2011

Keywords

  • Compact symmetric spaces
  • Even multiplicity
  • Fundamental solution
  • Gauss sum
  • Schödinger equation
  • Shift operator
  • Support

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Support theorem for the fundamental solution to the Schrödinger equation on certain compact symmetric spaces'. Together they form a unique fingerprint.

  • Cite this