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Characteristic functions of almost solvable extensions of Hermitian operators

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Abstract

The characteristic operator-functions W(λ) are studied of the almost solvable extensions of an Hermitian operator. The inverse problem is solved, a multiplication theorem is proved, and a formula is derived expressing W(λ) in terms of the Weyl function and the boundary operator. Characteristic functions are computed of various differential and difference operators, with the help of which are proved theorems of the completeness of the systems of proper and adjoint vectors.

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Authors and Affiliations

  1. Makeevka Engineering-Construction Institute, USSR

    V. A. Derkach & M. M. Malamud

  2. Donetsk Polytechnic Institute, USSR

    V. A. Derkach & M. M. Malamud

Authors
  1. V. A. Derkach
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  2. M. M. Malamud
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 435–459, April, 1992.

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Derkach, V.A., Malamud, M.M. Characteristic functions of almost solvable extensions of Hermitian operators. Ukr Math J 44, 379–401 (1992). https://doi.org/10.1007/BF01064871

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  • DOI: https://doi.org/10.1007/BF01064871

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