Dissertationes Mathematicae最新文献_第2页

Mackey groups and Mackey topologies 麦基组和麦基拓扑

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2021-01-01 DOI: 10.4064/dm835-7-2021

L. Außenhofer, D. Dikranjan

引用次数: 2

Homotopical properties of hyperspaces of generalized continua: the proper and ordinary cases 广义连续体的超空间的同调性质:一般和适当情况

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2021-01-01 DOI: 10.4064/dm820-6-2021

W. J. Charatonik, T. Fernández-Bayort, A. Quintero

引用次数: 1

Approximate roots of quasi-ordinary polynomials 拟普通多项式的近似根

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2021-01-01 DOI: 10.4064/dm841-12-2021

B. Gryszka

引用次数: 0

There is no bound on Borel classes of graphs in the Luzin–Novikov theorem 在Luzin-Novikov定理中，图的Borel类没有界

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2020-09-27 DOI: 10.4064/dm831-11-2021

P. Holický, M. Zelený

引用次数: 0

Holomorphic function spaces on homogeneous Siegel domains 齐次Siegel域上的全纯函数空间

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2020-09-23 DOI: 10.4064/dm833-3-2021

Mattia Calzi, M. Peloso

引用次数: 16

Conditional positive definiteness in operator theory 算子理论中的条件正确定性

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2020-08-21 DOI: 10.4064/dm846-1-2022

Zenon Jan Jablo'nski, I. Jung, J. Stochel

{"title":"Conditional positive definiteness in operator theory","authors":"Zenon Jan Jablo'nski, I. Jung, J. Stochel","doi":"10.4064/dm846-1-2022","DOIUrl":"https://doi.org/10.4064/dm846-1-2022","url":null,"abstract":"In this paper we extensively investigate the class of conditionally positive definite operators, namely operators generating conditionally positive definite sequences. This class itself contains subnormal operators, $2$- and $3$-isometries and much more beyond them. Quite a large part of the paper is devoted to the study of conditionally positive definite sequences of exponential growth with emphasis put on finding criteria for their positive definiteness, where both notions are understood in the semigroup sense. As a consequence, we obtain semispectral and dilation type representations for conditionally positive definite operators. We also show that the class of conditionally positive definite operators is closed under the operation of taking powers. On the basis of Agler's hereditary functional calculus, we build an $L^{infty}(M)$-functional calculus for operators of this class, where $M$ is an associated semispectral measure. We provide a variety of applications of this calculus to inequalities involving polynomials and analytic functions. In addition, we derive new necessary and sufficient conditions for a conditionally positive definite operator to be a subnormal contraction (including a telescopic one).","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2020-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42661046","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

Harmonic analysis on graphs via Bratteli diagrams and path-space measures 基于Bratteli图和路径空间测度的图的调和分析

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2020-07-30 DOI: 10.4064/dm826-12-2021

S. Bezuglyi, P. Jorgensen

{"title":"Harmonic analysis on graphs via Bratteli diagrams and path-space measures","authors":"S. Bezuglyi, P. Jorgensen","doi":"10.4064/dm826-12-2021","DOIUrl":"https://doi.org/10.4064/dm826-12-2021","url":null,"abstract":"The past decade has seen a flourishing of advances in harmonic analysis of graphs. They lie at the crossroads of graph theory and such analytical tools as graph Laplacians, Markov processes and associated boundaries, analysis of path-space, harmonic analysis, dynamics, and tail-invariant measures. Motivated by recent advances for the special case of Bratteli diagrams, our present focus will be on those graph systems $G$ with the property that the sets of vertices $V$ and edges $E$ admit discrete level structures. A choice of discrete levels in turn leads to new and intriguing discrete-time random-walk models. \u0000Our main extension (which greatly expands the earlier analysis of Bratteli diagrams) is the case when the levels in the graph system $G$ under consideration are now allowed to be standard measure spaces. Hence, in the measure framework, we must deal with systems of transition probabilities, as opposed to incidence matrices (for the traditional Bratteli diagrams). \u0000The paper is divided into two parts, (i) the special case when the levels are countable discrete systems, and (ii) the (non-atomic) measurable category, i.e., when each level is a prescribed measure space with standard Borel structure. The study of the two cases together is motivated in part by recent new results on graph-limits. Our results depend on a new analysis of certain duality systems for operators in Hilbert space; specifically, one dual system of operator for each level. We prove new results in both cases, (i) and (ii); and we further stress both similarities, and differences, between results and techniques involved in the two cases.","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2020-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49284953","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

Construction and heat kernel estimates of generalstable-like Markov processes 类广义马尔可夫过程的构造和热核估计

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2020-05-18 DOI: 10.4064/dm824-8-2021

V. Knopova, A. Kulik, R. Schilling

{"title":"Construction and heat kernel estimates of general\u0000stable-like Markov processes","authors":"V. Knopova, A. Kulik, R. Schilling","doi":"10.4064/dm824-8-2021","DOIUrl":"https://doi.org/10.4064/dm824-8-2021","url":null,"abstract":"A stable-like process is a Feller process $(X_t)_{tgeq 0}$ taking values in $mathbb{R}^d$ and whose generator behaves, locally, like an $alpha$-stable Levy process, but the index $alpha$ and all other characteristics may depend on the state space. More precisely, the jump measure need not to be symmetric and it strongly depends on the current state of the process; moreover, we do not require the gradient term to be dominated by the pure jump part. Our approach is to understand the above phenomena as suitable microstructural perturbations. \u0000We show that the corresponding martingale problem is well-posed, and its solution is a strong Feller process which admits a transition density. For the transition density we obtain a representation as a sum of an explicitly given principal term -- this is essentially the density of an $alpha$-stable random variable whose parameters depend on the current state $x$ -- and a residual term; the $L^inftyotimes L^1$-norm of the residual term is negligible and so is, under an additional structural assumption, the $L^inftyotimes L^infty$-norm. Concrete examples illustrate the relation between the assumptions and possible transition density estimates.","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43104907","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: 17

CP-semigroups and dilations, subproduct systems and superproduct systems: the multi-parameter case and beyond cp -半群与膨胀，子积系统与超积系统:多参数情况及其他

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2020-03-11 DOI: 10.4064/dm823-5-2022

O. Shalit, Michael Skeide

{"title":"CP-semigroups and dilations, subproduct systems and superproduct systems: the multi-parameter case and beyond","authors":"O. Shalit, Michael Skeide","doi":"10.4064/dm823-5-2022","DOIUrl":"https://doi.org/10.4064/dm823-5-2022","url":null,"abstract":"These notes are the output of a decade of research on how the results about dilations of one-parameter CP-semigroups with the help of product systems, can be put forward to d-parameter semigroups - and beyond. While preliminary work on the two- and d-parameter case is based on the approach via the Arveson-Stinespring correspondence of a CP-map by Muhly and Solel (and limited to von Neumann algebras), here we explore consequently the approach via Paschke's GNS-correspondence of a CP-map by Bhat and Skeide. (A comparison is postponed to Appendix A(iv).) \u0000The generalizations are multi-fold, the difficulties often enormous. In fact, our only true if-and-only-if theorem, is the following: A Markov semigroup over (the opposite of) an Ore monoid admits a full (strict or normal) dilation if and only if its GNS-subproduct system embeds into a product system. Already earlier, it has been observed that the GNS- (respectively, the Arveson-Stinespring) correspondences form a subproduct system, and that the main difficulty is to embed that into a product system. Here we add, that every dilation comes along with a superproduct system (a product system if the dilation is full). The latter may or may not contain the GNS-subproduct system; it does, if the dilation is strong - but not only. \u0000Apart from the many positive results pushing forward the theory to large extent, we provide plenty of counter examples for almost every desirable statement we could not prove. Still, a small number of open problems remains. The most prominent: Does there exist a CP-semigroup that admits a dilation, but no strong dilation? Another one: Does there exist a Markov semigroup that admits a (necessarily strong) dilation, but no full dilation?","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2020-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46076386","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

Fans in the theory of real semigroups 实半群理论中的粉丝

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/dm819-6-2020

M. Dickmann, A. Petrovich

引用次数: 0