Siberian Mathematical Journal

, Volume 56, Issue 3, pp 442–454 | Cite as

Convergence conditions for interpolation rational fractions with finitely many poles

  • A. G. LipchinskiĭEmail author


We consider an interpolation process for the class of functions with finitely many singular points by means of rational functions whose poles coincide with the singular points of the function under interpolation. The interpolation nodes form a triangular matrix. We find necessary and sufficient conditions for the uniform convergence of the sequence of interpolation fractions to the function under interpolation on every compact set disjoint from the singular points of the function and other conditions for convergence. We generalize and improve the familiar results on the interpolation of functions with finitely many singular points by rational fractions and of entire functions by polynomials.


analytic function singularity of a function interpolation process rational fraction uniform convergence convergence conditions 


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© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.P. P. Ershov Ishim State Pedagogical Institute IshimTyumen’ RegionRussia

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