{"id":"https://openalex.org/W7214567126","doi":"https://doi.org/10.48550/arxiv.2609.31805","title":"Hahn-Type Orthogonality for the Resolvent Delta Operator $\\mathscr L=D(I-D)^{-1}$","display_name":"Hahn-Type Orthogonality for the Resolvent Delta Operator $\\mathscr L=D(I-D)^{-1}$","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214567126","doi":"https://doi.org/10.48550/arxiv.2609.31805"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.31805","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31805","pdf_url":"https://arxiv.org/pdf/2609.31805","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/2609.31805","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009909232","display_name":"Youssef Esstafa","orcid":"https://orcid.org/0009-0002-8880-9463","observed_orcids":["https://orcid.org/0009-0002-8880-9463","https://orcid.org/0000-0002-8148-2878"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Esstafa, Youssef","raw_affiliation_strings":["LMM"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMM","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085011185","display_name":"Ridha Sfaxi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sfaxi, Ridha","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9965999722480774,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9965999722480774,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.0006000000284984708,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/appell-sequences","display_name":"Appell sequences","score":0.7649999856948853},{"id":"https://openalex.org/keywords/orthogonal-polynomial-sequences","display_name":"orthogonal polynomial systems","score":0.6869999766349792},{"id":"https://openalex.org/keywords/rigidity-theorems","display_name":"rigidity theorems","score":0.7940000295639038},{"id":"https://openalex.org/keywords/structural-relationships","display_name":"structural relationships","score":0.9279999732971191},{"id":"https://openalex.org/keywords/generating-functions","display_name":"generating functions","score":0.5680000185966492}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7997000217437744},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.6581000089645386},{"id":"https://openalex.org/C108408018","wikidata":"https://www.wikidata.org/wiki/Q1124546","display_name":"Laguerre polynomials","level":2,"score":0.6391000151634216},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.635200023651123},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5485000014305115},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5376999974250793},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.5217999815940857},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.5181999802589417},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5097000002861023},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4934999942779541},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.4871000051498413},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.4717999994754791},{"id":"https://openalex.org/C115633367","wikidata":"https://www.wikidata.org/wiki/Q5254796","display_name":"Delta operator","level":5,"score":0.4359999895095825},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4156999886035919},{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.4133000075817108},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.33959999680519104},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.33869999647140503},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.3231000006198883},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.30649998784065247},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.3043000102043152},{"id":"https://openalex.org/C54486999","wikidata":"https://www.wikidata.org/wiki/Q209675","display_name":"Dirac delta function","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.29409998655319214},{"id":"https://openalex.org/C6128204","wikidata":"https://www.wikidata.org/wiki/Q847600","display_name":"Entire function","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2572999894618988},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.31805","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31805","pdf_url":"https://arxiv.org/pdf/2609.31805","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":"pmh:oai:HAL:hal-05764115v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05764115v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2609.31805","doi":"https://doi.org/10.48550/arxiv.2609.31805","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.31805","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.31805","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31805","pdf_url":"https://arxiv.org/pdf/2609.31805","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214567126.pdf","grobid_xml":"https://content.openalex.org/works/W7214567126.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2567806540"],"related_works":["https://openalex.org/W585614028","https://openalex.org/W6981921366","https://openalex.org/W2590540466","https://openalex.org/W2126165512","https://openalex.org/W2066240595","https://openalex.org/W2529920061","https://openalex.org/W2075094826","https://openalex.org/W7214645906","https://openalex.org/W2996107654","https://openalex.org/W4321435503"],"abstract_inverted_index":{"We":[0,35],"investigate":[1],"orthogonality":[2,77,125],"under":[3],"the":[4,39,45,54,76,90,109,112],"shift-invariant":[5],"resolvent":[6,113],"delta":[7],"operator":[8,114],"$\\mathscr":[9,23],"L=D(I-D)^{-1}$.":[10],"First,":[11],"we":[12],"prove":[13],"a":[14,17,31,67,81,86,97,101,105],"rigidity":[15,63],"theorem:":[16],"monic":[18],"orthogonal":[19],"polynomial":[20],"sequence":[21],"is":[22,30],"L$-Appell":[24],"if":[25,28],"and":[26,42,94,104,123],"only":[27],"it":[29],"translated":[32,82,87],"Laguerre":[33,83],"sequence.":[34],"then":[36],"move":[37],"beyond":[38],"Appell":[40],"setting":[41,118],"show":[43],"that":[44,66],"diagonal":[46,91],"family":[47],"associated":[48],"with":[49],"$$\\mathcal":[50],"S_\u03b2=\\frac\u03b2{\u03b2+1}\\mathcal":[51],"L^0+\\frac{1}{\u03b2+1}\u03b4$$":[52],"satisfies":[53],"exact":[55,129],"Hahn":[56],"relation":[57,70],"$$\\mathscr":[58],"L":[59,72],"B_{n+1}(x;\u03b2)=(n+1)B_n(x;\u03b2+1).$$":[60],"A":[61],"second":[62],"result":[64],"shows":[65],"single":[68],"pointwise":[69],"$P_{n+1}(c)=\u03b8\\,\\mathscr":[71],"P_{n+1}(c)$":[73],"already":[74],"forces":[75],"functional":[78,84],"to":[79],"be":[80],"or":[85],"member":[88],"of":[89],"family.":[92],"Connection":[93],"structure":[95],"relations,":[96],"semiclassical":[98,124],"Pearson":[99],"equation,":[100],"differential":[102],"characterization,":[103],"generating":[106],"function":[107],"complete":[108],"description.":[110],"Thus":[111],"provides":[115],"an":[116],"explicit":[117],"in":[119],"which":[120],"delta-operator":[121],"lowering":[122],"are":[126],"linked":[127],"by":[128],"structural":[130],"identities.":[131]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-28T00:00:00"}
