{"doi":"10.4153/cmb-1993-054-8","title":"Some Properties of Hankel Convolution Operators","abstract":"<jats:title>Abstract</jats:title><jats:p>Let <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline01\" /> be the Zemanian space of Hankel transformable generalized functions and let <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline02\" /> be the space of Hankel convolution operators for <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline01\" />. This <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline01\" /> is the dual of a subspace <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline03\" /> of <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline02\" /> for which <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline02\" /> is also the space of Hankel convolutors. In this paper the elements of <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline02\" /> are characterized as those in <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline04\" /> and in <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline05\" /> that commute with Hankel translations. Moreover, necessary and sufficient conditions on the generalized Hankel transform <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline06\" /> are established in order that every <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline07\" /> such that <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline08\" /> in <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline03\" /> .</jats:p>","journal":"Canadian Mathematical Bulletin","year":1993,"id":616858,"datarank":1.6470566983815202,"base_score":3.332204510175204,"endowment":3.332204510175204,"self_citation_contribution":0.49983067652628066,"citation_network_contribution":1.1472260218552395,"self_endowment_contribution":0.49983067652628066,"citer_contribution":1.1472260218552395,"corpus_percentile":null,"corpus_rank":null,"citation_count":27,"citer_count":14,"citers_with_citation_signal":9,"citers_with_endowment":9,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1349055,"name":"I. Marrero","orcid":"0000-0003-3732-9929","position":1,"is_corresponding":false},{"id":152609,"name":"J. J. Betancor","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"resolved":true,"title":"Some Properties of Hankel Convolution Operators","abstract":"<jats:title>Abstract</jats:title><jats:p>Let <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline01\" /> be the Zemanian space of Hankel transformable generalized functions and let <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline02\" /> be the space of Hankel convolution operators for <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline01\" />. This <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline01\" /> is the dual of a subspace <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline03\" /> of <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline02\" /> for which <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline02\" /> is also the space of Hankel convolutors. In this paper the elements of <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline02\" /> are characterized as those in <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline04\" /> and in <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline05\" /> that commute with Hankel translations. Moreover, necessary and sufficient conditions on the generalized Hankel transform <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline06\" /> are established in order that every <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline07\" /> such that <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline08\" /> in <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500013795_inline03\" /> .</jats:p>","is_dataset_classified":null,"base_score":3.332204510175204,"endowment":3.332204510175204,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"19767382","pmcid":null,"openalex_id":"https://openalex.org/W2330799166","authors":[],"funders":[],"total_grants":0,"fwci":2.8291,"citation_percentile":0.91188728,"influential_citations":0,"citation_trend":[{"year":2021,"count":2},{"year":2022,"count":1},{"year":2023,"count":1},{"year":2024,"count":1},{"year":2025,"count":3}],"oa_status":"bronze","license":"https://www.cambridge.org/core/terms","oa_locations":[{"url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/225B91B9F72F2227BB9E5FB84FB73802/S0008439500013795a.pdf/div-class-title-some-properties-of-hankel-convolution-operators-div.pdf","host_type":"journal"},{"url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/225B91B9F72F2227BB9E5FB84FB73802/S0008439500013795a.pdf/div-class-title-some-properties-of-hankel-convolution-operators-div.pdf","host_type":"publisher"},{"url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0008439500013795","host_type":"publisher"},{"url":"https://doi.org/10.4153/cmb-1993-054-8","host_type":"journal"}],"fields_of_study":["Mathematical Analysis and Transform Methods","Mathematical functions and polynomials","Approximation Theory and Sequence Spaces"],"mesh_terms":[],"keywords":["Hankel transform","Mathematics","Hankel matrix","Convolution (computer science)","Convolution power","Subspace topology","Space (punctuation)","Circular convolution","Pure mathematics","Convolution theorem","Mathematical analysis","Algebra over a field","Bessel function","Fourier transform","Computer science"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-08-03T00:07:15.497613Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}