On discrete holomorphic Paley–Wiener spaces and sampling on the square lattice

A. Monguzzi; M. Monti

doi:10.1090/tran/9644

March 2, 2026Transactions of the American Mathematical Society

On discrete holomorphic Paley–Wiener spaces and sampling on the square lattice

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Key Points

This work aims to characterize a reproducing kernel Hilbert space of discrete entire functions on the square lattice.
Analyzed a reproducing kernel Hilbert space of discrete entire functions.
Investigated the properties of the space in relation to the classical Paley–Wiener space.
Developed a sampling result for the discrete functions.
Provided a Paley–Wiener type characterization for the space.
Outlined the characteristics of the space similar to those in the classical Paley–Wiener framework.
Demonstrated effective sampling results for discrete entire functions on the square lattice.

Implication

This research explores discrete entire functions, revealing characteristics and sampling methods in a square lattice, suggesting new mathematical insights.

Abstract

We consider a reproducing kernel Hilbert space of discrete entire functions on the square lattice Z 2 Z^2 inspired by the classical Paley–Wiener space of entire functions of exponential growth in the complex plane. For such space we provide a Paley–Wiener type characterization and a sampling result.

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Monguzzi et al. (2026) studied this question.

synapsesocial.com/papers/69a7ccb2d48f933b5eed865f https://doi.org/10.1090/tran/9644

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On discrete holomorphic Paley–Wiener spaces and sampling on the square lattice

Key Points

Implication

Abstract

Discussion

Cite This Study

On discrete holomorphic Paley–Wiener spaces and sampling on the square lattice

Key Points

Implication

Abstract

Discussion

Cite This Study

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