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Updated: Nov 15, 2025

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Published on: April 12, 2019
Multiple Sampling and Interpolation in Weighted Fock Spaces of Entire Functions.
Luis Alberto Escudero1, Antti Haimi1, José Luis Romero1,2
1Acoustics Research Institute, Austrian Academy of Sciences, Wohllebengasse 12-14, 1040 Vienna, Austria.
This study characterizes sampling and interpolating sets in weighted Fock spaces using weighted Beurling densities. These densities provide a precise measure for understanding set properties in complex analysis.
Area of Science:
- Complex Analysis
- Functional Analysis
Background:
- Weighted Fock spaces are crucial in complex analysis.
- Sampling and interpolating sets are fundamental concepts for function reconstruction.
Purpose of the Study:
- To characterize sampling and interpolating sets within weighted Fock spaces.
- To establish a connection between set properties and their weighted Beurling densities.
Main Methods:
- Analysis of sets in weighted Fock spaces on the complex plane.
- Application of weighted Beurling densities for characterization.
Main Results:
- Established criteria for sampling and interpolating sets based on weighted Beurling densities.
- Provided a quantitative framework for understanding these sets.
Conclusions:
- Weighted Beurling densities offer an effective tool for analyzing sampling and interpolating sets.
- The findings contribute to the theory of function spaces and signal processing.
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