{"title":"Approximation of polynomial hulls by analytic varieties: a counterexample.","authors":"Tobias Harz","doi":"10.1007/s40627-025-00192-y","DOIUrl":"https://doi.org/10.1007/s40627-025-00192-y","url":null,"abstract":"<p><p>We construct a connected, compact set <math><mrow><mi>K</mi> <mo>⊂</mo> <msup><mrow><mi>C</mi></mrow> <mn>2</mn></msup> </mrow> </math> with the following property: there exist points <math><mrow><mi>p</mi> <mo>∈</mo> <mover><mi>K</mi> <mo>^</mo></mover> <mo></mo> <mi>K</mi></mrow> </math> such that there does not exist a sequence <math><mrow><mo>{</mo> <msub><mi>A</mi> <mi>ν</mi></msub> <mo>}</mo></mrow> </math> of analytic sets <math> <mrow><msub><mi>A</mi> <mi>ν</mi></msub> <mo>⊂</mo> <mo>⊂</mo> <msup><mrow><mi>C</mi></mrow> <mn>2</mn></msup> </mrow> </math> with boundary satisfying <math><mrow><mi>p</mi> <mo>∈</mo> <msub><mi>A</mi> <mi>ν</mi></msub> </mrow> </math> for every <math><mrow><mi>ν</mi> <mo>∈</mo> <mi>N</mi></mrow> </math> and <math> <mrow><msub><mo>lim</mo> <mrow><mi>ν</mi> <mo>→</mo> <mi>∞</mi></mrow> </msub> <mi>b</mi> <msub><mi>A</mi> <mi>ν</mi></msub> <mo>⊂</mo> <mi>K</mi></mrow> </math> . For every point in <math> <mrow><mover><mi>K</mi> <mo>^</mo></mover> <mo></mo> <mi>K</mi></mrow> </math> , we explicitly construct a sequence of Poletsky discs, and we compute the weak limit of the pushforwards of the Green current under these discs.</p>","PeriodicalId":87237,"journal":{"name":"Complex analysis and its synergies","volume":"12 2","pages":"16"},"PeriodicalIF":0.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13526089/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148868359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Picard-type theorem and the solutions of certain ODE and PDE","authors":"Goutam Haldar, Molla Basir Ahamed","doi":"10.1007/s40627-024-00142-0","DOIUrl":"https://doi.org/10.1007/s40627-024-00142-0","url":null,"abstract":"","PeriodicalId":87237,"journal":{"name":"Complex analysis and its synergies","volume":"1 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141816426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hardy spaces of meta-analytic functions and the Schwarz boundary value problem","authors":"William L. Blair","doi":"10.1007/s40627-024-00139-9","DOIUrl":"https://doi.org/10.1007/s40627-024-00139-9","url":null,"abstract":"","PeriodicalId":87237,"journal":{"name":"Complex analysis and its synergies","volume":"16 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141354144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sarika Verma, Raj Kumar, Om P. Ahuja, A. Çetinkaya
{"title":"q-Analog of prestarlike functions","authors":"Sarika Verma, Raj Kumar, Om P. Ahuja, A. Çetinkaya","doi":"10.1007/s40627-024-00137-x","DOIUrl":"https://doi.org/10.1007/s40627-024-00137-x","url":null,"abstract":"","PeriodicalId":87237,"journal":{"name":"Complex analysis and its synergies","volume":"65 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140755476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Turán type inequalities for the generalized derivative of a polynomial","authors":"F. A. Bhat, H. A. Dar","doi":"10.1007/s40627-024-00135-z","DOIUrl":"https://doi.org/10.1007/s40627-024-00135-z","url":null,"abstract":"","PeriodicalId":87237,"journal":{"name":"Complex analysis and its synergies","volume":"113 34","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140380298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On perturbations of singular complex analytic curves","authors":"Achinta Kumar Nandi","doi":"10.1007/s40627-024-00133-1","DOIUrl":"https://doi.org/10.1007/s40627-024-00133-1","url":null,"abstract":"","PeriodicalId":87237,"journal":{"name":"Complex analysis and its synergies","volume":"108 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140223621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kalyan Barman, Bikash Chakraborty, Raymond Mortini
{"title":"Two classical formulas for the sum of powers of consecutive integers via complex analysis","authors":"Kalyan Barman, Bikash Chakraborty, Raymond Mortini","doi":"10.1007/s40627-024-00131-3","DOIUrl":"https://doi.org/10.1007/s40627-024-00131-3","url":null,"abstract":"","PeriodicalId":87237,"journal":{"name":"Complex analysis and its synergies","volume":"15 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140412894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Inequalities for a class of $${mathcal {B}}_n$$-operators","authors":"Zahid Manzoor Wani, Wali Mohammad Shah","doi":"10.1007/s40627-023-00129-3","DOIUrl":"https://doi.org/10.1007/s40627-023-00129-3","url":null,"abstract":"","PeriodicalId":87237,"journal":{"name":"Complex analysis and its synergies","volume":"76 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140483986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Local CR-diffeomorphisms of CR-quadrics of codimension two. I. Standard Hermitian quadrics","authors":"N. G. Kruzhilin","doi":"10.1007/s40627-023-00127-5","DOIUrl":"https://doi.org/10.1007/s40627-023-00127-5","url":null,"abstract":"","PeriodicalId":87237,"journal":{"name":"Complex analysis and its synergies","volume":"85 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138965147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Radius of γdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$gamma $$end{document}-spirallikeness of order αdocumentc","authors":"S. Kazımoğlu, Kamaljeet Gangania","doi":"10.1007/s40627-023-00125-7","DOIUrl":"https://doi.org/10.1007/s40627-023-00125-7","url":null,"abstract":"","PeriodicalId":87237,"journal":{"name":"Complex analysis and its synergies","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139233628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}