Complete discrete Schoenberg-Delsarte theory for homogeneous spaces

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Autori principali:	Damase, Sujit Sakharam, Pascoe, James Eldred
Natura:	Preprint
Pubblicazione:	2026
Soggetti:	Functional Analysis Classical Analysis and ODEs Metric Geometry Operator Algebras Representation Theory 43A35, 15B48, 46L07, 52C17, 47A20
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author	Damase, Sujit Sakharam Pascoe, James Eldred
author_facet	Damase, Sujit Sakharam Pascoe, James Eldred
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2602_09010
institution	arXiv
publishDate	2026
record_format	arxiv
spellingShingle	Complete discrete Schoenberg-Delsarte theory for homogeneous spaces Damase, Sujit Sakharam Pascoe, James Eldred Functional Analysis Classical Analysis and ODEs Metric Geometry Operator Algebras Representation Theory 43A35, 15B48, 46L07, 52C17, 47A20 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.
title	Complete discrete Schoenberg-Delsarte theory for homogeneous spaces
topic	Functional Analysis Classical Analysis and ODEs Metric Geometry Operator Algebras Representation Theory 43A35, 15B48, 46L07, 52C17, 47A20
url	https://arxiv.org/abs/2602.09010

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