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Jentzsch‐Szegö Type Theorems for the Zeros of Best Approximants
Author(s) -
Blatt H.-P.,
Saff E. B.,
Simkani M.
Publication year - 1988
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-38.2.307
Subject(s) - mathematics , type (biology) , polynomial function theorems for zeros , pure mathematics , mathematical analysis , geology , polynomial , alternating polynomial , paleontology , matrix polynomial
Let E be a compact set in the complex plane C having connected and regular complement. For a nonentire function f analytic in the interior of E and continuous on E , we investigate the limiting distribution of the zeros of the sequence of polynomials{ p n ∗ } 1 ∞of best uniform approximation to f on E . The zeros of best L p polynomial approximants and best uniform rational approximants having a bounded number of free poles are also considered.