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The Carleman property of the resolvent of a one-dimensional Dirac operator with an integrable potential

Abstract

It is proved that the resolvent of a Dirac operator with a potential thai is integrable on the entire axis is a Carleman operator.

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Literature cited

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    Yu. M. Berezanskii,Expansions in Eigenfunctions of Selfadjoint Operators, American Mathematical Society, Providence (1968).

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    T. Kato, “Wave operators and similarity for certain nonself-adjoint operators,”Matematika,18, No. 3, 60–82 (1974).

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    I.-P. P. Syroid, “Nonself-adjoint perturbation of the continuous spectrum of a Dirac operator,”Ukr. Mat. Zh.,35, No. 1, 115–119 (1983).

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Additional information

Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 36, 1992, pp. 18–21.

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Syroid, I.-.P. The Carleman property of the resolvent of a one-dimensional Dirac operator with an integrable potential. J Math Sci 67, 3274–3276 (1993). https://doi.org/10.1007/BF01097729

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Keywords

  • Dirac Operator
  • Integrable Potential
  • Entire Axis
  • Carleman Operator