Approximation of analytical functions by $$k$$ k -positive linear operators in the closed domain

Approximation of analytical functions by $$k$$ k -positive linear operators in the closed... This work treats the problem of convergence for the sequences of linear $$k$$ k -positive operators on a space of functions that are analytic in a closed domain. By convergence in this space, we mean a uniform convergence in a closed domain that contains the original domain strictly inside itself, while the linear $$k$$ k -positive operators are naturally associated with Faber polynomials related to the considered domain. Until now, this problem has been solved in the space of functions analytic in an open bounded domain with the topology of compact convergence. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Approximation of analytical functions by $$k$$ k -positive linear operators in the closed domain

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Publisher
Springer Basel
Copyright
Copyright © 2013 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-013-0255-3
Publisher site
See Article on Publisher Site

Abstract

This work treats the problem of convergence for the sequences of linear $$k$$ k -positive operators on a space of functions that are analytic in a closed domain. By convergence in this space, we mean a uniform convergence in a closed domain that contains the original domain strictly inside itself, while the linear $$k$$ k -positive operators are naturally associated with Faber polynomials related to the considered domain. Until now, this problem has been solved in the space of functions analytic in an open bounded domain with the topology of compact convergence.

Journal

PositivitySpringer Journals

Published: Oct 8, 2013

References

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