Interpolation and sampling sequences for mixed-norm spaces
Phuc K. Nguyen, Daniel H. Luecking (University of Arkansas)
TL;DR
This paper extends the characterization of interpolation and sampling sequences from Bergman spaces to mixed-norm spaces, addressing the challenges posed by the lack of conformal invariance.
Contribution
It provides new criteria for interpolation and sampling sequences specifically tailored for mixed-norm spaces, which differ from Bergman spaces.
Findings
New characterization of interpolation sequences in mixed-norm spaces
New criteria for sampling sequences in mixed-norm spaces
Different proof techniques due to lack of conformal invariance
Abstract
This paper extends the known characterization of interpolation and sampling sequences for Bergman spaces to the mixed-norm spaces. The Bergman spaces have conformal invariance properties not shared by the mixed-norm spaces. As a result, different techniques of proof were required.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Holomorphic and Operator Theory · Algebraic and Geometric Analysis