Approximation and Interpolation Applied to Entire Functions |
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a₁ Applying theorem approximating polynomials arc of length arg z asymptotic directions belong bounded region C₁ class of R-functions combinaties van functies constants d₁ converges uniformly Conversely every entire Corollary d₂ dk 9 double-sector entire function f(z exponential type finite limit-point fo(z follows function of exponential functions all zeros h₁ h₂ Hence f(z lemma Let f Let f(z Let the sequence LEVINSON limit-function f(z monotonic function N. G. DE BRUIJN number of zeros OBRECHKOFF partial sums PÓLYA polynomials fn(z positive integer Proof of theorem prove regular ROUCHÉ'S theorem satisfy the conditions sector with aperture sequence of points sequence of polynomials sequence zn sets R satisfying smaller type suppose Szász tending to infinity theorem 14 Theorem 4.1 vertex warg WEISNER z/zp zero type zeros of fn(z zm II 1-z/zp