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Radial bounds for Schrödinger operators in euclidean domains

  • David Gurarie
  • Gerhard Kalisch
  • Mark Kon
  • Edward Landesman
Research Articles
  • 2.6k Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 1475)

Abstract

We extend study of regularity properties of elliptic operators (c.f. [2]) to second order operators on domains bounded by finite numbers of hyperplanes. Previous results for Euclidean space and the symmetry of the domains are exploited to obtain resolvent bounds. Corollaries include semigroup generation, essential self-adjointness, and regularity of eigenfunction expansions for such operators. The present work provides basic results aimed at extending regularity information for partial differential operators (especially with singular coefficients) to a general class of operators in domains with boundary. In one dimension these results encompass a body of work in Sturm-Liouville theory on the half-line.

Keywords

Elliptic Operator Regularity Property Partial Differential Operator Convolution Kernel Eigenfunction Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Copson, E.T. (1965): Asymptotic Expansions. Cambridge University Press, LondonCrossRefzbMATHGoogle Scholar
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    Gurarie, D., Kon, M. (1984): Radial bounds for perturbations of elliptic operators. J. Functional Analysis 56, 99–123MathSciNetCrossRefzbMATHGoogle Scholar
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    Gurarie, D. (1984): Kernels of elliptic operators: bounds and summability. J. Differential Equations 55, 1–29MathSciNetCrossRefzbMATHGoogle Scholar
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    Levitan, B.M., Sargsjan, I.S. (1975): Introduction to Spectral Theory: Self-Adjoint Ordinary Differential Operators. American Mathematical Society, ProvidencezbMATHGoogle Scholar
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    Titchmarsh, E. (1946): Eigenfunction Expansions Associated with Second Order Differential Equations. Vol. I, II. Oxford University Press, OxfordzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • David Gurarie
  • Gerhard Kalisch
  • Mark Kon
  • Edward Landesman

There are no affiliations available

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