Fundamental solution of hyperbolic differential operators and the poisson summation formula

نویسندگان

  • Norbert Ortner
  • Peter Wagner
  • Norbert ORTNER
  • Peter WAGNER
چکیده

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. The attempt to subsume the summation of the double series (1) under a more general framework led to a systematic investigation of the existence and the uniqueness of fundamental solutions of linear hyperbolic partial differential operators with constant coefficients on tori and of their Fourier expansiolls. The restriction to the class of hyperbolic operators implies a representation of the fundamelltal solution by a locally finite series; further restriction to strictly hyperbolic operators yields colwergence results in the scale HQ(Tn) of Sobolev spaces on the torus Tn. Finally, we apply the theory to some specific many-dimensional series involving Bessel functions.

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تاریخ انتشار 2013