Local Growth of Weierstrass Σ-function and Whittaker-type Derivative Sampling
نویسندگان
چکیده
Two explicit guard functions Kj = Kj(δz), j = 1, 2, are obtained, which depend on the distance δz between z and the nearest point of the integer lattice in the complex plane, such that δzK1(δz) ≤ |σ(z)|e−π|z|2/2 ≤ δzK2(δz), z ∈ C, where σ(z) stands for the Weierstraß σ-function. This result is used to improve the circular truncation error upper bound in the qth order Whittaker-type derivative sampling for the Leont’ev functions space [2, πq 2 ), q ≥ 1. 2000 Mathematics Subject Classification: 30D15, 30E10, 94A20; Secondary: 30A10, 41A05, 94A12.
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