{"id":{"repo_id":"wichita-thes","oai_identifier":"oai:soar.wichita.edu:10057/16383"},"canonical_url":"https://search.dev.ndltd.org/etd/wichita-thes/oai:soar.wichita.edu:10057/16383","repository":{"repo_id":"wichita-thes","name":"Wichita State University","base_url":"https://soar.wichita.edu/oai/request"},"display":{"title":"Isotropic positive definite functions on spheres generated from those in Euclidean spaces","abstract":"In this thesis, author have reviewed the classical characterizations of isotropic positive definite functions on Euclidean spaces and spheres, and had applied them to develop a construction of isotropic positive de nite functions on spheres. However, this construction only works when the dimension of the sphere is odd. The next work is to develop isotropic positive de nite functions on all spheres.","abstract_html":"In this thesis, author have reviewed the classical characterizations of isotropic positive definite functions on Euclidean spaces and spheres, and had applied them to develop a construction of isotropic positive de nite functions on spheres. However, this construction only works when the dimension of the sphere is odd. The next work is to develop isotropic positive de nite functions on all spheres.","abstract_has_math":false,"creators":["Nie, Zhihui"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-05","date_published":"2019-05","updated_at":"2026-07-24T06:06:46Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/16383"],"render_values":[{"text":"hdl:10057/16383","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2019-05"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/16383"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["In this thesis, author have reviewed the classical characterizations of isotropic positive definite functions on Euclidean spaces and spheres, and had applied them to develop a construction of isotropic positive de nite functions on spheres. However, this construction only works when the dimension of the sphere is odd. The next work is to develop isotropic positive de nite functions on all spheres."]},{"key":"dc:title","label":"Title","values":["Isotropic positive definite functions on spheres generated from those in Euclidean spaces"]}]}],"canonical_facts":{"dc:date.issued":["2019-05"],"dc:description.other":["In this thesis, author have reviewed the classical characterizations of isotropic positive definite functions on Euclidean spaces and spheres, and had applied them to develop a construction of isotropic positive de nite functions on spheres. However, this construction only works when the dimension of the sphere is odd. The next work is to develop isotropic positive de nite functions on all spheres."],"dc:identifier":["hdl:10057/16383"],"dc:title":["Isotropic positive definite functions on spheres generated from those in Euclidean spaces"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T06:06:46Z"}