Integral Operators Basic in Random Fields Estimation Theory

Alexander Kozhevnikov; Alexander G. Ramm

paper

Integral Operators Basic in Random Fields Estimation Theory

arXiv:math-ph/0405002

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 integra $o p er a t or o v er ab o u n d e dd o main$ Ω $in$ {\Bbb R}^{n} $i s w e ak l y s in g u l a r . T hi so p er a t or i s ani so m or p hi s mb e tw ee na pp r o p r ia t e S o b o l e v s p a ces . T hi s i s p r o v e d b y a r e d u c t i o n o f t h e in t e g r a l e q u$ an elliptic boundary value problem in the domain exterior to $Ω.$ Extra difficulties arise due to the fact that the exterior boundary value problem should be solved in the Sobolev spaces of negative order.