{"title":"Pseudo $S$-Asymptotically Bloch Type Periodicity with Applications to Some Evolution Equations","authors":"Yong-Kui Chang, Yanyan Wei","doi":"10.4171/ZAA/1671","DOIUrl":"https://doi.org/10.4171/ZAA/1671","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":"26 1","pages":"33-50"},"PeriodicalIF":1.2,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83675216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Existence and Uniqueness of Positive Solutions for a Singular Second-Order Integral Boundary Value Problem","authors":"J. Caballero, B. López, K. Sadarangani","doi":"10.4171/ZAA/1672","DOIUrl":"https://doi.org/10.4171/ZAA/1672","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":"48 1","pages":"51-65"},"PeriodicalIF":1.2,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85578911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The index of a selfadjoint Fredholm operator is zero by the well-known fact that the kernel of a selfadjoint operator is perpendicular to its range. The Fredholm index was generalised to families by Atiyah and Janich in the sixties, and it is readily seen that on complex Hilbert spaces this so called index bundle vanishes for families of selfadjoint Fredholm operators as in the case of a single operator. The first aim of this note is to point out that for every real Hilbert space and every compact topological space $X$ there is a family of selfadjoint Fredholm operators parametrised by $Xtimes S^1$ which has a non-trivial index bundle. Further, we use this observation and a family index theorem of Pejsachowicz to study multiparameter bifurcation of homoclinic solutions of Hamiltonian systems, where we generalise a previously known class of examples.
{"title":"The index bundle for selfadjoint Fredholm operators and multiparameter bifurcation for Hamiltonian systems","authors":"R. Skiba, Nils Waterstraat","doi":"10.4171/zaa/1718","DOIUrl":"https://doi.org/10.4171/zaa/1718","url":null,"abstract":"The index of a selfadjoint Fredholm operator is zero by the well-known fact that the kernel of a selfadjoint operator is perpendicular to its range. The Fredholm index was generalised to families by Atiyah and Janich in the sixties, and it is readily seen that on complex Hilbert spaces this so called index bundle vanishes for families of selfadjoint Fredholm operators as in the case of a single operator. The first aim of this note is to point out that for every real Hilbert space and every compact topological space $X$ there is a family of selfadjoint Fredholm operators parametrised by $Xtimes S^1$ which has a non-trivial index bundle. Further, we use this observation and a family index theorem of Pejsachowicz to study multiparameter bifurcation of homoclinic solutions of Hamiltonian systems, where we generalise a previously known class of examples.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49466806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Differentiating Orlicz Spaces with Rectangles Having Fixed Shapes in a Set of Directions","authors":"E. D’Aniello, L. Moonens","doi":"10.4171/zaa/1668","DOIUrl":"https://doi.org/10.4171/zaa/1668","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":"20 1","pages":"461-473"},"PeriodicalIF":1.2,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82405994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Global Wellposedness and Large Time Behavior of Solutions to the Hall-Magnetohydrodynamics Equations","authors":"Xiaoping Zhai","doi":"10.4171/zaa/1665","DOIUrl":"https://doi.org/10.4171/zaa/1665","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":"14 1","pages":"395-419"},"PeriodicalIF":1.2,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73823046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For any $A(z),B(z),C(z)inmathbb{C}[z]$, we study the zero distribution of a table of polynomials $left{ P_{m,n}(z)right} _{m,ninmathbb{N}_{0}}$ satisfying the recurrence relation [ P_{m,n}(z)=A(z)P_{m-1,n}(z)+B(z)P_{m,n-1}(z)+C(z)P_{m-1,n-1}(z) ] with the initial condition $P_{0,0}(z)=1$ and $P_{-m,-n}(z)=0$ $forall m,ninmathbb{N}$. We show that the zeros of $P_{m,n}(z)$ lie on a curve whose equation is given explicitly in terms of $A(z),B(z)$, and $C(z)$. We also study the zero distribution of a case with a general initial condition.
{"title":"Zeros of a table of polynomials satisfying a four-term contiguous relation","authors":"Jack Luong, Khang Tran","doi":"10.4171/zaa/1698","DOIUrl":"https://doi.org/10.4171/zaa/1698","url":null,"abstract":"For any $A(z),B(z),C(z)inmathbb{C}[z]$, we study the zero distribution of a table of polynomials $left{ P_{m,n}(z)right} _{m,ninmathbb{N}_{0}}$ satisfying the recurrence relation [ P_{m,n}(z)=A(z)P_{m-1,n}(z)+B(z)P_{m,n-1}(z)+C(z)P_{m-1,n-1}(z) ] with the initial condition $P_{0,0}(z)=1$ and $P_{-m,-n}(z)=0$ $forall m,ninmathbb{N}$. We show that the zeros of $P_{m,n}(z)$ lie on a curve whose equation is given explicitly in terms of $A(z),B(z)$, and $C(z)$. We also study the zero distribution of a case with a general initial condition.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44699539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Partial Regularity Results for Quasimonotone Elliptic Systems with General Growth","authors":"B. Stroffolini","doi":"10.4171/zaa/1662","DOIUrl":"https://doi.org/10.4171/zaa/1662","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":"35 1","pages":"315-347"},"PeriodicalIF":1.2,"publicationDate":"2020-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79778841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let $X = [0,1]^{n}$, $n geq1$. We show that the typical (in the sense of Baire category) compact subset of $X$ is not only a zero dimensional Cantor space but it satisfies the property of being strongly microscopic, which is stronger than being of dimension zero.
{"title":"On some Generic Small Cantor Spaces","authors":"E. D’Aniello, M. Maiuriello","doi":"10.4171/ZAA/1660","DOIUrl":"https://doi.org/10.4171/ZAA/1660","url":null,"abstract":"Let $X = [0,1]^{n}$, $n geq1$. We show that the typical (in the sense of Baire category) compact subset of $X$ is not only a zero dimensional Cantor space but it satisfies the property of being strongly microscopic, which is stronger than being of dimension zero.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":"35 1","pages":"277-288"},"PeriodicalIF":1.2,"publicationDate":"2020-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76667839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"New Fixed Point Theorem for Discontinuous Operators in Cones and Applications","authors":"Jorge Rodríguez–López","doi":"10.4171/zaa/1654","DOIUrl":"https://doi.org/10.4171/zaa/1654","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":"91 1","pages":"131-150"},"PeriodicalIF":1.2,"publicationDate":"2020-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80409661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonlocal Averages in Space and Time Given by Medians and the Mean Curvature Flow","authors":"Gastón Beltritti, J. Rossi","doi":"10.4171/zaa/1658","DOIUrl":"https://doi.org/10.4171/zaa/1658","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":"3 1","pages":"223-243"},"PeriodicalIF":1.2,"publicationDate":"2020-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79334694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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