A study of the rate of rational approximation of a class of analytic functions
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This paper is devoted to results belonging to the theory of rational approximation of analytic functions. We study the rate of decrease of the best approximations ρn of a functionf holomorphic in a disk ¦z ∶ ¦z¦< ρ, ρ>1> by rational functions of order at most n in the uniform metric on the unit disk with center at z=0. We prove theorems that connect the rate of decrease of the quantities ρn with the order σ≥0 and type Τ≥0 of the functionf. The proofs of these results are based on the methods of the theory of Hankel operators.
KeywordsRational Function Analytic Function Unit Disk Rational Approximation Hankel Operator
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