Non-uniformly flat affine algebraic hypersurfaces
Vamsi Pingali, Dror Varolin
TL;DR
This paper explores the interpolation and separation properties of non-uniformly flat affine algebraic hypersurfaces in Bargmann-Fock spaces, providing examples and analyzing their interpolation capabilities.
Contribution
It introduces four smooth affine algebraic hypersurfaces that are not uniformly flat and determines which are interpolating, advancing understanding in higher dimensions.
Findings
Two of the four hypersurfaces are interpolating.
Non-uniform flatness does not preclude interpolation.
Provides explicit examples in higher dimensions.
Abstract
The relationship between interpolation and separation properties of hypersurfaces in Bargmann-Fock spaces over is not well-understood except for . We present four examples of smooth affine algebraic hypersurfaces that are not uniformly flat, and show that exactly two of them are interpolating.
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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Advanced Harmonic Analysis Research