Abstract
We characterize sampling and interpolating sets with derivatives in weighted Fock spaces on the complex plane in terms of their weighted Beurling densities.
Highlights
1.1 Results and ContextLet φ : C → R be a subharmonic function with Laplacian bounded above and below by positive constants
We study sampling and interpolation on weighted Fock spaces, where we sample or interpolate using the function values, and the values of its derivatives
We characterize the sets that allow for multiple sampling and interpolation in weighted Fock spaces in terms of certain densities, provided that the number of derivatives considered at each sampling point is bounded
Summary
Let φ : C → R be a subharmonic function with Laplacian bounded above and below by positive constants. The weighted Fock space of entire functions is Communicated by Uwe Kähler. This article is part of the topical collection “Linear Operators and Linear System” edited by Sanne ter Horst, Dmitry S.
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