Approximation and Interpolation Applied to Entire Functions1949 - Functions - 55 pages |
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a₁ Applying theorem arbitrary complex numbers arc of length arg z asymptotic directions bounded region C₁ CARTWRIGHT class of R-functions constants d₁ converges uniformly Conversely every entire Corollary d₂ double-sector exponential type finite limit-point formal power-series function of exponential functions all zeros h₁ h₂ half-lines with directions half-plane R(z Hence f(z lemma Let f(z Let R consist Let the sequence LEVINSON limit-function f(z LINDWART monotonic function N. G. DE BRUIJN number of zeros partial sums PÓLYA polynomials fn polynomials fn z positive integer Proof of theorem regular ROUCHÉ's theorem satisfy the conditions sector with aperture sequence of points sequence of polynomials smaller type suppose Szász tending to infinity theorem 14 theorem 5.1 type of f(z vertex warg z/zp z₁ zap runs zero type zeros of fn(z zm II 1-z/zp