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Local growth of Weierstrass σ-function and Whittaker-type derivative sampling

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 𝑞-th order Whittaker-type derivative sampling for the Leont'ev functions space.

circular truncation error ; derivative sampling ; entire function spaces [ρ, 𝜓], [ρ, 𝜓) ; sampling truncation error upper bound ; Weierstrass σ-function ; Whittaker-type derivative sampling reconstruction

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