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Normed versus topological groups: dichotomy and duality 规范群与拓扑群:二分法和对偶性
IF 1.8 3区 数学
Dissertationes Mathematicae Pub Date : 2010-01-01 DOI: 10.4064/DM472-0-1
N. Bingham, A. Ostaszewski
{"title":"Normed versus topological groups: dichotomy and duality","authors":"N. Bingham, A. Ostaszewski","doi":"10.4064/DM472-0-1","DOIUrl":"https://doi.org/10.4064/DM472-0-1","url":null,"abstract":"The key vehicle of the recent development of a topological theory of regular variation based on topological dynamics [BO-TI], and embracing its classical univariate counterpart (cf. [BGT]) as well as fragmentary multivariate (mostly Euclidean) theories (eg [MeSh], [Res], [Ya]), are groups with a right-invariant metric carrying flows. Following the vector paradigm, they are best seen as normed groups. That concept only occasionally appears explicitly in the literature despite its frequent disguised presence, and despite a respectable lineage traceable back to the Pettis closed-graph theorem, to the Birkhoff-Kakutani metrization theorem and further back still to Banach's Theorie des operations lineaires. Its most recent noteworthy appearance has been in connection with the Effros Open Mapping Principle. We collect together known salient features and develop their theory including Steinhaus theory unified by the Category Embedding Theorem [BO-LBII], the associated themes of subadditivity and convexity, and a topological duality inherent to topological dynamics. We study the latter both for its independent interest and as a foundation for topological regular variation.","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70156170","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}
引用次数: 52
Complex absorbing potential method for systems 系统的复吸收势法
IF 1.8 3区 数学
Dissertationes Mathematicae Pub Date : 2010-01-01 DOI: 10.4064/DM469-0-1
J. Kungsman, M. Melgaard
{"title":"Complex absorbing potential method for systems","authors":"J. Kungsman, M. Melgaard","doi":"10.4064/DM469-0-1","DOIUrl":"https://doi.org/10.4064/DM469-0-1","url":null,"abstract":"The Complex Absorbing Potential (CAP) method is widely used to compute resonances in Quantum Chemistry, both for scalar valued and matrix valued Hamiltonians. In the semiclassical limit h → 0 we consider resonances near the real axis and we establish the CAP method rigorously in an abstract matrix valued setting by proving that resonances are perturbed eigenvalues of the nonselfadjoint CAP Hamiltonian, and vice versa. The proof is based on pseudodifferential operator theory and microlocal analysis.","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70156105","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}
引用次数: 4
Weighted inequalities for gradients on non-smooth domains 非光滑域上梯度的加权不等式
IF 1.8 3区 数学
Dissertationes Mathematicae Pub Date : 2010-01-01 DOI: 10.4064/DM471-0-1
C. Sweezy, J. Wilson
{"title":"Weighted inequalities for gradients on non-smooth domains","authors":"C. Sweezy, J. Wilson","doi":"10.4064/DM471-0-1","DOIUrl":"https://doi.org/10.4064/DM471-0-1","url":null,"abstract":"We prove weighted norm inequalities of integral type between the gradients of solutions u of elliptic equations and their boundary data f on bounded Lipschitz domains. 0. Introduction. We are interested in the following general question: To what extent is the interior smoothness of the solution of a PDE controlled by the size of its boundary values? To be more specific, suppose (for now) that Ω ⊂ R is a nice domain, μ is a positive measure supported in Ω, and v is a non-negative measurable function defined on ∂Ω. If f : ∂Ω → R is reasonable (say, continuous function with compact support), we let u : Ω → R be the solution of the classical Dirichlet problem with boundary values equal to f . (We are implicitly assuming that Ω is nice enough to have this make sense!) Let p and q be real numbers lying strictly between 1 and infinity. When is it the case that (∫ Ω |∇u|q dμ )1/q ≤ (∫","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70156152","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}
引用次数: 1
Approximate amenability of semigroup algebras and Segal algebras 半群代数和西格代数的近似可适应性
IF 1.8 3区 数学
Dissertationes Mathematicae Pub Date : 2010-01-01 DOI: 10.4064/DM474-0-1
H. Dales, R. J. Loy
{"title":"Approximate amenability of semigroup algebras and Segal algebras","authors":"H. Dales, R. J. Loy","doi":"10.4064/DM474-0-1","DOIUrl":"https://doi.org/10.4064/DM474-0-1","url":null,"abstract":"In recent years, there have been several studies of various `approximate' versions of the key notion of amenability, which is defined for all Banach algebras; these studies began with work of Ghahramani and Loy in 2004. The present memoir continues such work: we shall define various notions of approximate amenability, and we shall discuss and extend the known background, which considers the relationships between different versions of approximate amenability. There are a number of open questions on these relationships; these will be considered. In Chapter 1, we shall give all the relevant definitions and a number of basic results, partly surveying existing work; we shall concentrate on the case of Banach function algebras. In Chapter 2, we shall discuss these properties for the semigroup algebra `1(S) of a semigroup S. In the case where S has only finitely many idempotents, `1(S) is approximately amenable if and only if it is amenable. In Chapter 3, we shall consider the class of weighted semigroup algebras of the form `1(N^; !), where ! : Z ! [1; 1) is an arbitrary function. We shall determine necessary and sufficient conditions on ! for these Banach sequence algebras to have each of the various approximate amenability properties that interest us. In this way we shall illuminate the implications between these properties. In Chapter 4, we shall discuss Segal algebras on T and on R. It is a conjecture that every proper Segal algebra on T fails to be approximately amenable; we shall establish this conjecture for a wide class of Segal algebras.","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70156222","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}
引用次数: 35
Componentwise and Cartesian decompositions of linear relations 线性关系的分量分解和笛卡尔分解
IF 1.8 3区 数学
Dissertationes Mathematicae Pub Date : 2009-06-01 DOI: 10.4064/DM465-0-1
S. Hassi, H. D. Snoo, F. H. Szafraniec
{"title":"Componentwise and Cartesian decompositions of linear relations","authors":"S. Hassi, H. D. Snoo, F. H. Szafraniec","doi":"10.4064/DM465-0-1","DOIUrl":"https://doi.org/10.4064/DM465-0-1","url":null,"abstract":"Let $A$ be a, not necessarily closed, linear relation in a Hilbert space $sH$ with a multivalued part $mul A$. An operator $B$ in $sH$ with $ran Bperpmul A^{**}$ is said to be an operator part of $A$ when $A=B hplus ({0}times mul A)$, where the sum is componentwise (i.e. span of the graphs). This decomposition provides a counterpart and an extension for the notion of closability of (unbounded) operators to the setting of linear relations. Existence and uniqueness criteria for the existence of an operator part are established via the so-called canonical decomposition of $A$. In addition, conditions are developed for the decomposition to be orthogonal (components defined in orthogonal subspaces of the underlying space). Such orthogonal decompositions are shown to be valid for several classes of relations. The relation $A$ is said to have a Cartesian decomposition if $A=U+I V$, where $U$ and $V$ are symmetric relations and the sum is operatorwise. The connection between a Cartesian decomposition of $A$ and the real and imaginary parts of $A$ is investigated.","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70156278","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}
引用次数: 66
Refined Kodaira classes and conductors of twisted elliptic curves 改进了扭椭圆曲线的Kodaira类和导体
IF 1.8 3区 数学
Dissertationes Mathematicae Pub Date : 2009-01-01 DOI: 10.4064/DM463-0-1
J. Browkin, Daniel Davies
{"title":"Refined Kodaira classes and conductors of twisted elliptic curves","authors":"J. Browkin, Daniel Davies","doi":"10.4064/DM463-0-1","DOIUrl":"https://doi.org/10.4064/DM463-0-1","url":null,"abstract":"","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70156188","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}
引用次数: 0
On the analysis of boundary value problems in nonsmooth domains 非光滑区域边值问题的分析
IF 1.8 3区 数学
Dissertationes Mathematicae Pub Date : 2009-01-01 DOI: 10.4064/DM462-0-1
G. Fremiot, W. Horn, A. Laurain, Murali Rao, J. Sokołowski
{"title":"On the analysis of boundary value problems in nonsmooth domains","authors":"G. Fremiot, W. Horn, A. Laurain, Murali Rao, J. Sokołowski","doi":"10.4064/DM462-0-1","DOIUrl":"https://doi.org/10.4064/DM462-0-1","url":null,"abstract":"","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70156178","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}
引用次数: 41
The complex Monge–Ampère operator 复monge - ampantere算子
IF 1.8 3区 数学
Dissertationes Mathematicae Pub Date : 2009-01-01 DOI: 10.4064/DM466-0-1
R. Czyż
{"title":"The complex Monge–Ampère operator","authors":"R. Czyż","doi":"10.4064/DM466-0-1","DOIUrl":"https://doi.org/10.4064/DM466-0-1","url":null,"abstract":"","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70156355","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}
引用次数: 15
Homogeneity, non-smooth atoms and Besov spaces of generalised smoothness on quasi-metric spaces 准度量空间上的均匀性、非光滑原子和广义光滑的Besov空间
IF 1.8 3区 数学
Dissertationes Mathematicae Pub Date : 2009-01-01 DOI: 10.4064/DM460-0-1
A. Caetano, Sofia Lopes
{"title":"Homogeneity, non-smooth atoms and Besov spaces of generalised smoothness on quasi-metric spaces","authors":"A. Caetano, Sofia Lopes","doi":"10.4064/DM460-0-1","DOIUrl":"https://doi.org/10.4064/DM460-0-1","url":null,"abstract":"","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70156139","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}
引用次数: 4
Weighted convolution algebras on subsemigroups of the real line 实线子半群上的加权卷积代数
IF 1.8 3区 数学
Dissertationes Mathematicae Pub Date : 2009-01-01 DOI: 10.4064/DM459-0-1
H. Dales, H. V. Dedania
{"title":"Weighted convolution algebras on subsemigroups of the real line","authors":"H. Dales, H. V. Dedania","doi":"10.4064/DM459-0-1","DOIUrl":"https://doi.org/10.4064/DM459-0-1","url":null,"abstract":"","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4064/DM459-0-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70156103","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}
引用次数: 16
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