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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On analytic continuability of the missing Cauchy datum for Helmholtz boundary problems
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by Mirza Karamehmedović PDF
Proc. Amer. Math. Soc. 143 (2015), 1515-1530 Request permission

Abstract:

We relate the domains of analytic continuation of Dirichlet and Neumann boundary data for Helmholtz problems in two or more independent variables. The domains are related à priori, locally and explicitly in terms of complex polyrectangular neighbourhoods of planar pieces of the boundary. To this end we identify and characterise a special subspace of the standard pseudodifferential operators with real-analytic symbols. The result is applicable in the estimation of the domain of analytic continuation of solutions across planar pieces of the boundary.
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Additional Information
  • Mirza Karamehmedović
  • Affiliation: Department of Applied Mathematics and Computer Science, Technical University of Denmark, Matematiktorvet 303B, DK-2800 Kgs. Lyngby, Denmark
  • Received by editor(s): May 19, 2010
  • Received by editor(s) in revised form: November 17, 2012
  • Published electronically: December 22, 2014
  • Communicated by: Richard Rochberg
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 1515-1530
  • MSC (2010): Primary 35S05
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12103-4
  • MathSciNet review: 3314066