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Exact propagators for some degenerate hyperbolic operators

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Arkiv för Matematik

Abstract

Exact propagators are obtained for the degenerate second order hyperbolic operators ∂2 t -t 2lΔ x , l=1,2,..., by analytic continuation from the degenerate elliptic operators ∂2 t +t 2lΔ x . The partial Fourier transforms are also obtained in closed form, leading to integral transform formulas for certain combinations of Bessel functions and modified Bessel functions.

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Authors and Affiliations

  1. Department of Mathematics, Yale University, New Haven, CT, 06520-8383, USA

    Richard Beals

  2. Department of Mathematics, Weizmann Institute of Science, Rehevot, 76100, Israel

    Yakar Kannai

Authors
  1. Richard Beals
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  2. Yakar Kannai
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Correspondence to Richard Beals or Yakar Kannai.

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Beals, R., Kannai, Y. Exact propagators for some degenerate hyperbolic operators. Ark Mat 44, 191–209 (2006). https://doi.org/10.1007/s11512-006-0018-5

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  • DOI: https://doi.org/10.1007/s11512-006-0018-5

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