Integral Operators Basic in Random Fields Estimation Theory
نویسنده
چکیده
1 2 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 Ω in Rn 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 Ω. Extra difficulties arise due to the fact that the exterior boundary value problem should be solved in the Sobolev spaces of negative order.
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