IJPAM: Volume 20, No. 3 (2005)


Alexander Kozhevnikov$^1$, Alexander G. Ramm$^2$
$^1$Department of Mathematics
University of Haifa
Mount Carmel, Haifa, 31905, ISRAEL
e-mail: kogevn@math.haifa.ac.il
$^2$Department of Mathematics
Kansas State University
Manhattan, KS 66506-2602, USA
e-mail: ramm@math.ksu.edu
url: https://www.math.ksu.edu/$\sim$ramm

Abstract.The paper deals with the basic integral equation of random field estimation theory by the criterion of minimum of variance of the error estimate. This integral equation is of the first kind. The corresponding integral operator over a bounded domain $\Omega $ in ${\Bbb R} ^{n}$ is weakly singular. This operator is an isomorphism between appropriate Sobolev spaces. This is proved by a reduction of the integral equation to an elliptic boundary value problem in the domain exterior to $\Omega $. Extra difficulties arise due to the fact that the exterior boundary value problem should be solved in the Sobolev spaces of negative order.

Received: April 18, 2005

AMS Subject Classification: 35S15, 35R30, 45B05, 45P05, 62M09, 62M40

Key Words and Phrases: integral equations, pseudodifferential operators, random fields estimation, boundary-value problems, Fredholm operator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 20
Issue: 3