{"id":"https://openalex.org/W7204883117","doi":"https://doi.org/10.48550/arxiv.2608.28801","title":"Complex Analysis in completeness, spectral and scattering problems","display_name":"Complex Analysis in completeness, spectral and scattering problems","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204883117","doi":"https://doi.org/10.48550/arxiv.2608.28801"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28801","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28801","pdf_url":"https://arxiv.org/pdf/2608.28801","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/2608.28801","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053068048","display_name":"Alexei Poltoratski","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Poltoratski, Alexei","raw_affiliation_strings":["University of Wisconsin , Department of Mathematics , Van Vleck Hall , 480 Lincoln Drive , Madison , WI 53706 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin , Department of Mathematics , Van Vleck Hall , 480 Lincoln Drive , Madison , WI 53706 , USA","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053068048"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.8794000148773193,"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"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.8794000148773193,"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"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.08330000191926956,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.01899999938905239,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/completeness-problem","display_name":"completeness problem","score":0.7829999923706055},{"id":"https://openalex.org/keywords/spectral-theory","display_name":"spectral theory","score":0.6010000109672546},{"id":"https://openalex.org/keywords/scattering-theory","display_name":"scattering theory","score":0.9940000176429749},{"id":"https://openalex.org/keywords/differential-operators","display_name":"differential operators","score":0.9449999928474426},{"id":"https://openalex.org/keywords/gap-problem","display_name":"gap problem","score":0.8550000190734863},{"id":"https://openalex.org/keywords/inverse-spectral-problem","display_name":"inverse spectral problem","score":0.9319999814033508},{"id":"https://openalex.org/keywords/schrodinger-operators","display_name":"Schr\u00f6dinger operators","score":0.9980000257492065},{"id":"https://openalex.org/keywords/canonical-hamiltonian-systems","display_name":"canonical Hamiltonian systems","score":0.9919999837875366},{"id":"https://openalex.org/keywords/nonlinear-fourier-transform","display_name":"nonlinear Fourier transform","score":0.8169999718666077},{"id":"https://openalex.org/keywords/pointwise-convergence","display_name":"pointwise convergence","score":0.9089999794960022},{"id":"https://openalex.org/keywords/harmonic-analysis","display_name":"harmonic analysis","score":0.8320000171661377},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.9900000095367432}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6773999929428101},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6455000042915344},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.590399980545044},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.5889999866485596},{"id":"https://openalex.org/C27156116","wikidata":"https://www.wikidata.org/wiki/Q1778098","display_name":"Pointwise convergence","level":3,"score":0.574400007724762},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.5419999957084656},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.5249999761581421},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5231999754905701},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.5210000276565552},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.517799973487854},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.5163000226020813},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.507099986076355},{"id":"https://openalex.org/C67105901","wikidata":"https://www.wikidata.org/wiki/Q903737","display_name":"Scattering theory","level":3,"score":0.490200012922287},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.4702000021934509},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4530999958515167},{"id":"https://openalex.org/C129683796","wikidata":"https://www.wikidata.org/wiki/Q430450","display_name":"Microlocal analysis","level":4,"score":0.43959999084472656},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4016999900341034},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.3937000036239624},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.38029998540878296},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.37049999833106995},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.367900013923645},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.35910001397132874},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.35260000824928284},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3077000081539154},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.30720001459121704},{"id":"https://openalex.org/C35958075","wikidata":"https://www.wikidata.org/wiki/Q1425077","display_name":"Spectral theorem","level":3,"score":0.28450000286102295},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.27469998598098755},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C136628613","wikidata":"https://www.wikidata.org/wiki/Q17098188","display_name":"Inverse scattering transform","level":4,"score":0.26570001244544983},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26460000872612}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28801","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28801","pdf_url":"https://arxiv.org/pdf/2608.28801","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.2608.28801","doi":"https://doi.org/10.48550/arxiv.2608.28801","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28801","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:2608.28801","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28801","pdf_url":"https://arxiv.org/pdf/2608.28801","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/W7204883117.pdf","grobid_xml":"https://content.openalex.org/works/W7204883117.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1589506572","https://openalex.org/W1653487624","https://openalex.org/W2081940026","https://openalex.org/W2136322410","https://openalex.org/W2579478503","https://openalex.org/W2791887565","https://openalex.org/W3037253781","https://openalex.org/W3137172585","https://openalex.org/W4378388213","https://openalex.org/W4415090750","https://openalex.org/W7204225324"],"related_works":["https://openalex.org/W3214794228","https://openalex.org/W576692639","https://openalex.org/W23100461","https://openalex.org/W2592660791","https://openalex.org/W625146923","https://openalex.org/W3043413915","https://openalex.org/W1998590674","https://openalex.org/W1981502223","https://openalex.org/W563198126","https://openalex.org/W2951259626"],"abstract_inverted_index":{"These":[0],"lectures":[1],"are":[2],"aimed":[3],"at":[4],"junior":[5],"researchers":[6],"seeking":[7],"to":[8,17,50],"enter":[9],"the":[10,47,51,54,73],"field":[11],"of":[12,14,53,72],"applications":[13],"complex":[15],"analysis":[16],"harmonic":[18],"analysis,":[19,21],"Fourier":[20,75],"spectral":[22,60],"and":[23,29,41,45,56,65,69,83],"scattering":[24],"theory":[25],"for":[26,62],"differential":[27],"operators":[28,64],"related":[30],"fields.":[31],"Starting":[32],"with":[33,81],"classical":[34],"completeness":[35],"problems":[36,61],"posed":[37],"by":[38],"Bernstein,":[39],"Beurling":[40],"Malliavin,":[42],"Wiener,":[43],"Kolmogorov":[44],"Krein,":[46],"course":[48],"progresses":[49],"solutions":[52],"Gap":[55],"Type":[57],"Problems,":[58],"inverse":[59],"Schr\u00f6dinger":[63],"canonical":[66],"Hamiltonian":[67],"systems,":[68],"pointwise":[70],"convergence":[71],"non-linear":[74],"transform.":[76],"Each":[77],"lecture":[78],"is":[79],"supplemented":[80],"exercises":[82],"references.":[84]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
