Complete discrete Schoenberg-Delsarte theory for homogeneous spaces

Sujit Sakharam Damase; James Eldred Pascoe

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arXiv · 2602.09010

Complete discrete Schoenberg-Delsarte theory for homogeneous spaces

Sujit Sakharam Damase·James Eldred Pascoe

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Abstract

We develop a theory of partially defined complete positivity preservers, extending Schoenberg's classical characterization to functions defined only on discrete subsets or constrained domains. We frame the extension problem through the theory of completely positive maps on operator systems -- we characterize general partially defined completely positive definite functions on general homogeneous spaces. We apply our interpolation to constrained packing problems and Delsarte theory, where one uses positive definite functions on homogeneous spaces to obtain bounds on various packing problems. We prove the specific positive definite function witnesses that a code is sharp for constrained angle codes must be from polynomials.

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BibTeX RIS

Sujit Sakharam Damase, James Eldred Pascoe. 2026-02-09. Complete discrete Schoenberg-Delsarte theory for homogeneous spaces. https://arxiv.org/abs/2602.09010

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