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Local Growth of Weierstrass σ-Function and Whittaker-Type Derivative Sampling
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Tibor K. Pogány
Published/Copyright:
February 26, 2010
Abstract
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 
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Key words and phrases:: 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
Received: 2001-07-02
Revised: 2002-09-21
Published Online: 2010-02-26
Published in Print: 2003-March
© Heldermann Verlag
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Articles in the same Issue
- On One Theorem of S. Warschawski
- Investigation of Two-Dimensional Models of Elastic Prismatic Shell
- Branched Coverings and Minimal Free Resolution for Infinite-Dimensional Complex Spaces
- Operational Identities for Circular and Hyperbolic Functions and Their Generalizations
- Bi-Hamiltonian Structure as a Shadow of Non-Noether Symmetry
- On the Oscillation of Solutions of First Order Differential Equations with Retarded Arguments
- Combinatorial Homology in a Perspective of Image Analysis
- Internal Crossed Modules
- Cochain Operations Defining Steenrod ⌣𝑖-Products in the Bar Construction
- On Maximal 𝑜𝑡-Subsets of the Euclidean Plane
- Inversion of the Cauchy Integral Taken over the Double Periodic Line
- Singular Integrals in Weighted Lebesgue Spaces with Variable Exponent
- Local Growth of Weierstrass σ-Function and Whittaker-Type Derivative Sampling
- Sturm–Liouville and Focal Higher Order BVPs with Singularities in Phase Variables
- On Some Convexity Properties of Generalized Cesáro Sequence Spaces
