Theoretical analysis highlights open problems in extending variation-diminishing properties to infinite totally positive matrices, suggesting new directions for sampling theory.
How can the variation-diminishing property and the invertibility conditions of totally positive matrices be extended to infinite totally positive matrices? These questions arise in the context of sampling theory and time-frequency analysis. We discuss these open problems and provide some context and some hints.
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Karlheinz Gröchenig (2026) studied this question.
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