Siberian Mathematical Journal

, Volume 42, Issue 5, pp 926–935 | Cite as

Optimal Error of Analytic Continuation from a Finite Set with Inaccurate Data in Hilbert Spaces of Holomorphic Functions

  • L. S. Maergoiz
  • A. M. Fedotov


We consider the problem of analytic continuation with inaccurate data from a finite subset U of a domain D of Cn to a point z0DU for the functions f belonging to a bounded correctness set V in a Hilbert space H(D) of analytic functions in D. In the case when H(D) is a Hilbert space with a reproducing kernel, we find constructive formulas for calculating the optimal error, the optimal function, and the optimal linear algorithm for extrapolation to a point z0 for functions in V whose approximate values are given on a set U. Moreover, we study the asymptotics of the optimal error in the case when the errors of initial data vanish.


Hilbert Space Initial Data Analytic Function Holomorphic Function Analytic Continuation 
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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • L. S. Maergoiz
    • 1
  • A. M. Fedotov
    • 2
  1. 1.Krasnoyarsk State Academy of Architecture and BuildingKrasnoyarsk
  2. 2.The Institute of Computer TechnologiesNovosibirsk

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