The problem of continuation with least coanalytic deviation
by
Julii A. Dubinskii
Moscow Power Engineering Institute, Moscow 111250, Krasnokazarmennaja 14

Let G be the domain on the complex plane C^1, z=x+iy, withboundary and f_0(): C^1 be agiven function.We consider the problem of continuing the function f_0() from to G so that the continuation has the least deviation from the Sobolev subspace O^1_p(G) W^1_p(G) of analytic functions. More precisely, inthe set of all functions f(z) W^1_p(G), such that f(z)=f_0() on, we find a function (the best continuation) with minimum ``coanalyticdeviation''\mu_p(f)=||f(z)-f_a(z)||^p_W¹p(G)'where f_a(z) is the analytic component of f(z) for the direct decompositionL_p(G)=O_p(G)+ _z W ^^^  ^1_p(G).

Date received: June 12, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahv-11.