. For Banach algebras A and solutions u : [0 , 1] → A of u ′′ ( t ) + f ( u ( t )) + λu ′ ( t ) 2 = 0 , u (0) = 0 , u (1) = 0 , we prove symmetry of the spectrum σ ( u ( t )) , that is, σ ( u ( t )) = σ ( u (1 − t )) for all t ∈ [0 , 1] , whenever σ ( u ([0 , 1])) lies in a cone of the complex plane.
{"title":"Spectral symmetry of solutions of boundary value problems in Banach algebras","authors":"G. Herzog, Peer Ch. Kunstmann","doi":"10.4064/ap210520-4-10","DOIUrl":"https://doi.org/10.4064/ap210520-4-10","url":null,"abstract":". For Banach algebras A and solutions u : [0 , 1] → A of u ′′ ( t ) + f ( u ( t )) + λu ′ ( t ) 2 = 0 , u (0) = 0 , u (1) = 0 , we prove symmetry of the spectrum σ ( u ( t )) , that is, σ ( u ( t )) = σ ( u (1 − t )) for all t ∈ [0 , 1] , whenever σ ( u ([0 , 1])) lies in a cone of the complex plane.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70582741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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{"title":"Extended escaping set for meromorphic functions outside a countable set of transcendental singularities","authors":"P. Domínguez, M. A. Montes De Oca, G. Sienra","doi":"10.4064/ap190820-31-3","DOIUrl":"https://doi.org/10.4064/ap190820-31-3","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70579293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Metrical almost periodicity and applications","authors":"M. Kostić","doi":"10.4064/ap220510-15-11","DOIUrl":"https://doi.org/10.4064/ap220510-15-11","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70585049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A control problem involving time and state-dependent maximal monotone operators via Young measures","authors":"S. Saïdi","doi":"10.4064/ap220522-26-11","DOIUrl":"https://doi.org/10.4064/ap220522-26-11","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"45 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70585773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dependence between homogeneous components of polynomials with small degree of Poisson bracket","authors":"Daria Holik, M. Karaś","doi":"10.4064/ap210126-4-1","DOIUrl":"https://doi.org/10.4064/ap210126-4-1","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70582276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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