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Complex powers of degenerate differential operators connected with the Klein-Gordon-Fock operator

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Abstract

We develop a theory of complex powers of the generalized Klein-Gordon-Fock operator

$$ m^2 - \square - i\lambda \frac{{\partial ^2 }} {{\partial x_1^2 }},\lambda > 0. $$

. The negative powers of this operator are realized as potential-type integrals with nonstandard metrics, while positive powers inverse to negative ones are realized as approximative inverse operators.

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Authors and Affiliations

  1. Southern Federal University, ul. Mil’chakova 8a, Rostov-on-Don, 344090, Russia

    D. V. Vozhzhov & V. A. Nogin

Authors
  1. D. V. Vozhzhov
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  2. V. A. Nogin
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Correspondence to D. V. Vozhzhov.

Additional information

Original Russian Text © D.V. Vozhzhov and V.A. Nogin, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 9, pp. 3–13.

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Vozhzhov, D.V., Nogin, V.A. Complex powers of degenerate differential operators connected with the Klein-Gordon-Fock operator. Russ Math. 53, 1–9 (2009). https://doi.org/10.3103/S1066369X09090011

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  • DOI: https://doi.org/10.3103/S1066369X09090011

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