Russian Mathematics

, Volume 53, Issue 9, pp 1–9

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

Article

DOI: 10.3103/S1066369X09090011

Cite this article as:
Vozhzhov, D.V. & Nogin, V.A. Russ Math. (2009) 53: 1. doi:10.3103/S1066369X09090011

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.

Key words and phrases

potential-type operatorsymbolinverse operatorapproximative inverse operator

Copyright information

© Allerton Press, Inc. 2009

Authors and Affiliations

  1. 1.Southern Federal UniversityRostov-on-DonRussia