, Volume 53, Issue 9, pp 1-9
Date: 21 Aug 2009

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.

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