We study the following problem. Consider an open, bounded and connected set Omega in R^n and an open subset E in Ohm. Knowing the values of an analytic function f on E we want to find its value on Omega. The problem is not well posed in the sense of Hadamard. We find a stability estimate for f depending on the measure of E.
A CONTINUOUS DEPENDENCE RESULT IN THE ANALYTIC CONTINUATION PROBLEM / S. VESSELLA. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - STAMPA. - 11:(1999), pp. 695-703. [10.1515/form.1999.020]
A CONTINUOUS DEPENDENCE RESULT IN THE ANALYTIC CONTINUATION PROBLEM
VESSELLA, SERGIO
1999
Abstract
We study the following problem. Consider an open, bounded and connected set Omega in R^n and an open subset E in Ohm. Knowing the values of an analytic function f on E we want to find its value on Omega. The problem is not well posed in the sense of Hadamard. We find a stability estimate for f depending on the measure of E.
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