{"id":"https://openalex.org/W7204913993","doi":"https://doi.org/10.48550/arxiv.2608.29976","title":"The Pego Theorem for the Hilbert--Schmidt Class","display_name":"The Pego Theorem for the Hilbert--Schmidt Class","publication_year":2026,"publication_date":"2026-08-30","ids":{"openalex":"https://openalex.org/W7204913993","doi":"https://doi.org/10.48550/arxiv.2608.29976"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29976","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29976","pdf_url":"https://arxiv.org/pdf/2608.29976","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.29976","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018344435","display_name":"Yaogan Mensah","orcid":"https://orcid.org/0000-0002-0028-5515","observed_orcids":["https://orcid.org/0000-0002-0028-5515"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mensah, Yaogan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5018344435"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.6166999936103821,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.6166999936103821,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.16869999468326569,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.0934000015258789,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hilbert-schmidt-operators","display_name":"Hilbert-Schmidt operators","score":0.9900000095367432},{"id":"https://openalex.org/keywords/precompact-sets","display_name":"precompact sets","score":0.7860000133514404},{"id":"https://openalex.org/keywords/equicontinuity","display_name":"equicontinuity","score":0.7490000128746033},{"id":"https://openalex.org/keywords/locally-compact-abelian-groups","display_name":"locally compact abelian groups","score":0.9290000200271606},{"id":"https://openalex.org/keywords/compactness-of-operators","display_name":"operator compactness","score":0.4749999940395355}],"concepts":[{"id":"https://openalex.org/C182539199","wikidata":"https://www.wikidata.org/wiki/Q249092","display_name":"Equicontinuity","level":2,"score":0.9388999938964844},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7506999969482422},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.6037999987602234},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.555899977684021},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.550000011920929},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5102999806404114},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5023000240325928},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5016999840736389},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49149999022483826},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.3702999949455261},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.34850001335144043},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.33959999680519104},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C171636804","wikidata":"https://www.wikidata.org/wiki/Q1149458","display_name":"Compactness theorem","level":4,"score":0.33390000462532043},{"id":"https://openalex.org/C35958075","wikidata":"https://www.wikidata.org/wiki/Q1425077","display_name":"Spectral theorem","level":3,"score":0.3066999912261963},{"id":"https://openalex.org/C129301229","wikidata":"https://www.wikidata.org/wiki/Q741865","display_name":"Uniform continuity","level":3,"score":0.2896000146865845},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C24743483","wikidata":"https://www.wikidata.org/wiki/Q1154848","display_name":"Potential theory","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.2540999948978424},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29976","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29976","pdf_url":"https://arxiv.org/pdf/2608.29976","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.29976","doi":"https://doi.org/10.48550/arxiv.2608.29976","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29976","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.29976","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29976","pdf_url":"https://arxiv.org/pdf/2608.29976","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204913993.pdf","grobid_xml":"https://content.openalex.org/works/W7204913993.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7203486122"],"related_works":["https://openalex.org/W7203486122","https://openalex.org/W2089100414","https://openalex.org/W4404343333","https://openalex.org/W4412683973","https://openalex.org/W2499483262","https://openalex.org/W2485969418","https://openalex.org/W2412824543","https://openalex.org/W7106649254","https://openalex.org/W4394847022","https://openalex.org/W1995011657"],"abstract_inverted_index":{"This":[0],"paper":[1],"establishes":[2],"an":[3],"operator-theoretic":[4],"version":[5],"of":[6,13,30],"Pego's":[7],"compactness":[8],"theorem":[9],"within":[10],"the":[11,54],"framework":[12],"quantum":[14,62],"harmonic":[15],"analysis":[16],"on":[17,53],"general":[18],"locally":[19],"compact":[20],"abelian":[21],"phase":[22,56],"spaces.":[23],"We":[24,58],"show":[25],"that":[26],"a":[27],"bounded":[28],"set":[29],"Hilbert-Schmidt":[31],"operators":[32],"is":[33,40,50],"precompact":[34],"if":[35,38],"and":[36,46],"only":[37],"it":[39],"uniformly":[41,51],"equicontinuous":[42,52],"under":[43],"phase-space":[44],"shifts":[45],"its":[47],"Fourier-Weyl":[48],"transform":[49],"dual":[55],"space.":[57],"provide":[59],"applications":[60],"to":[61],"physics.":[63]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
