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Hasse–Schmidt derivations and Cayley–Hamilton theorem for exterior algebras 外代数的Hasse-Schmidt推导和Cayley-Hamilton定理
Functional Analysis and Geometry Pub Date : 2019-01-09 DOI: 10.1090/CONM/733/14739
Letterio Gatto, I. Scherbak
{"title":"Hasse–Schmidt derivations and Cayley–Hamilton\u0000 theorem for exterior algebras","authors":"Letterio Gatto, I. Scherbak","doi":"10.1090/CONM/733/14739","DOIUrl":"https://doi.org/10.1090/CONM/733/14739","url":null,"abstract":"Using the natural notion of {em Hasse--Schmidt derivations on an exterior algebra}, we relate two classical and seemingly unrelated subjects. The first is the celebrated Cayley--Hamilton theorem of linear algebra, \"{em each endomorphism of a finite-dimensional vector space is a root of its own characteristic polynomial}\", and the second concerns the expression of the bosonic vertex operators occurring in the representation theory of the (infinite-dimensional) Heinsenberg algebra.","PeriodicalId":432671,"journal":{"name":"Functional Analysis and Geometry","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132745585","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}
引用次数: 11
Toeplitz operators in polyanalytic Bergman type spaces 多解析Bergman型空间中的Toeplitz算子
Functional Analysis and Geometry Pub Date : 2018-07-30 DOI: 10.1090/CONM/733/14747
G. Rozenblum, N. Vasilevski
{"title":"Toeplitz operators in polyanalytic Bergman\u0000 type spaces","authors":"G. Rozenblum, N. Vasilevski","doi":"10.1090/CONM/733/14747","DOIUrl":"https://doi.org/10.1090/CONM/733/14747","url":null,"abstract":"We consider Toeplitz operators in Bergman and Fock type spaces of polyanalytic $L^2textup{-}$functions on the disk or on the half-plane with respect to the Lebesgue measure (resp., on $mathbb{C}$ with the plane Gaussian measure). The structure involving creation and annihilation operators, similar to the classical one present for the Landau Hamiltonian, enables us to reduce Toeplitz operators in true polyanalytic spaces to the ones in the usual Bergman type spaces, however with distributional symbols. This reduction leads to describing a number of properties of the operators in the title, which may differ from the properties of the usual Bergman-Toeplitz operators.","PeriodicalId":432671,"journal":{"name":"Functional Analysis and Geometry","volume":"240 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116390793","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}
引用次数: 9
Some binomial formulas for non-commuting operators 非交换算子的一些二项式公式
Functional Analysis and Geometry Pub Date : 2018-01-14 DOI: 10.1090/CONM/733/14743
P. Kuchment, S. Lvin
{"title":"Some binomial formulas for non-commuting\u0000 operators","authors":"P. Kuchment, S. Lvin","doi":"10.1090/CONM/733/14743","DOIUrl":"https://doi.org/10.1090/CONM/733/14743","url":null,"abstract":"Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second commutator $[D,[D,U]]$ is proportional to $U$. \u0000Operators $D=d/dx$ (differentiation) and $U$- multiplication by $e^{lambda x}$ or by $sin lambda x$ are basic examples, for which some of these relations appeared unexpectedly as byproducts of an authors' previous medical imaging research.","PeriodicalId":432671,"journal":{"name":"Functional Analysis and Geometry","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132185642","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}
引用次数: 2
Similarity of holomorphic matrices on 1-dimensional Stein spaces 一维Stein空间上全纯矩阵的相似性
Functional Analysis and Geometry Pub Date : 2017-10-30 DOI: 10.1090/CONM/733/14744
J. Leiterer
{"title":"Similarity of holomorphic matrices on\u0000 1-dimensional Stein spaces","authors":"J. Leiterer","doi":"10.1090/CONM/733/14744","DOIUrl":"https://doi.org/10.1090/CONM/733/14744","url":null,"abstract":"R. Guralnick [Linear Algebra Appl. 99, 85-96 (1988)] proved that two holomorphic matrices on a noncompact connected Riemann surface, which are locally holomorphically similar, are globally holomorphically similar. In the preprints [arXiv:1703.09524] and [arXiv:1703.09530], a generalization of this to arbitrary (possibly, nonsmooth) 1-dimensional Stein spaces was obtained. The present paper contains a revised version of the proof from [arXiv:1703.09524]. The method of this revised proof can be used also in the higher dimensional case, which will be the subject of a forthcoming paper.","PeriodicalId":432671,"journal":{"name":"Functional Analysis and Geometry","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129132158","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}
引用次数: 1
Sobolev, Besov and Paley-Wiener vectors in Banach and Hilbert spaces Banach和Hilbert空间中的Sobolev、Besov和pely - wiener向量
Functional Analysis and Geometry Pub Date : 2017-08-22 DOI: 10.1090/conm/733/14746
I. Pesenson
{"title":"Sobolev, Besov and Paley-Wiener vectors in\u0000 Banach and Hilbert spaces","authors":"I. Pesenson","doi":"10.1090/conm/733/14746","DOIUrl":"https://doi.org/10.1090/conm/733/14746","url":null,"abstract":"We consider Banach spaces equipped with a set of strongly continuous bounded semigroups satisfying certain conditions. Using these semigroups we introduce an analog of a modulus of continuity and define analogs of Besov norms. A generalization of a classical interpolation theorem is proven in which the role of Sobolev spaces is played by subspaces defined in terms of infinitesimal operators of these semigroups. We show that our assumptions about a given set of semigroups are satisfied in the case of a strongly continuous bounded representation of a Lie group. In the case of a unitary representation in a Hilbert space we consider an analog of the Laplace operator and use it to define Paley-Wiener vectors. It allows us to develop a generalization of the Shannon-type sampling in Paley-Wiener subspaces and to construct Paley-Wiener nearly Parseval frames in the entire Hilbert space. It is shown that Besov spaces defined previously in terms of the modulus of continuity can be described in terms of approximation by Paley-Wiener vectors and also in terms of the frame coefficients. Throughout the paper we extensively use theory of interpolation and approximation spaces. The paper ends with applications of our results to function spaces on homogeneous manifolds.","PeriodicalId":432671,"journal":{"name":"Functional Analysis and Geometry","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128044142","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}
引用次数: 6
Total positivity, Grassmannian and modified Bessel functions 总正性、格拉斯曼函数和修正贝塞尔函数
Functional Analysis and Geometry Pub Date : 2017-08-07 DOI: 10.1090/CONM/733/14736
V. Buchstaber, A. Glutsyuk
{"title":"Total positivity, Grassmannian and modified\u0000 Bessel functions","authors":"V. Buchstaber, A. Glutsyuk","doi":"10.1090/CONM/733/14736","DOIUrl":"https://doi.org/10.1090/CONM/733/14736","url":null,"abstract":"A rectangular matrix is called totally positive, if all its minors are positive. A point of a real Grassmanian manifold $G_{l,m}$ of $l$-dimensional subspaces in $mathbb R^m$ is called strictly totally positive, if one can normalize its Plucker coordinates to make all of them positive. The totally positive matrices and the subsets of strictly totally positive points in Grassmanian manifolds arise in many domains of mathematics, mechanics and physics. F.R.Gantmacher and M.G.Krein considered totally positive matrices in the context of classical mechanics. Total positivity was used for construction of solutions of the Kadomtsev-Petviashvili (KP) partial differential equation by T.M.Malanyuk, M.Boiti, F.Pemperini, A.Pogrebkov, Y.Kodama, L.Williams. Different problems of mathematics, mechanics and physics led to constructions of totally positive matrices due to many mathematicians, including F.R. Gantmacher, M.G.Krein, I.J.Schoenberg, S.Karlin, A.E.Postnikov and ourselves. In our case totally positive matrices were constructed for solution of problems on model of the overdamped Josephson effect in superconductivity and double confluent Heun equations. In our previous paper we have proved that certain determinants formed by modified Bessel functions of the first kind are positive on the positive semi-axis. In the present paper we give a new result: a construction of multidimensional families of totally positive matrices formed by values of modified Bessel functions with non-negative integer indices. Their columns are numerated by the indices of the modified Bessel functions, and their rows are numerated by their arguments.","PeriodicalId":432671,"journal":{"name":"Functional Analysis and Geometry","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115824251","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}
引用次数: 13
A new method of extension of local maps of Banach spaces. Applications and examples Banach空间局部映射的一种新扩展方法。应用和示例
Functional Analysis and Geometry Pub Date : 2017-06-24 DOI: 10.1090/conm/733/14733
G. Belitskii, Victoria Rayskin
{"title":"A new method of extension of local maps of\u0000 Banach spaces. Applications and examples","authors":"G. Belitskii, Victoria Rayskin","doi":"10.1090/conm/733/14733","DOIUrl":"https://doi.org/10.1090/conm/733/14733","url":null,"abstract":"A known classical method of extension of smooth local maps of Banach spaces uses smooth bump functions. However, such functions are absent in the majority of infinite-dimensional Banach spaces. This is an obstacle in the development of local analysis, in particular in the questions of extending local maps onto the whole space. We suggest an approach that substitutes bump functions with special maps, which we call blid maps. It allows us to extend smooth local maps from non-smooth spaces, such as $C^q[0,1], q=0,1,...$. As an example of applications, we show how to reconstruct a map from its derivatives at a point, for spaces possessing blid maps. We also show how blid maps can assist in finding global solutions to cohomological equations having linear transformation of argument.","PeriodicalId":432671,"journal":{"name":"Functional Analysis and Geometry","volume":"461 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125812014","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}
引用次数: 6
A remark on the intersection of plane curves 关于平面曲线相交的注解
Functional Analysis and Geometry Pub Date : 2017-04-02 DOI: 10.1090/CONM/733/14737
C. Ciliberto, F. Flamini, M. Zaidenberg
{"title":"A remark on the intersection of plane\u0000 curves","authors":"C. Ciliberto, F. Flamini, M. Zaidenberg","doi":"10.1090/CONM/733/14737","DOIUrl":"https://doi.org/10.1090/CONM/733/14737","url":null,"abstract":"Let $D$ be a very general curve of degree $d=2ell-epsilon$ in $mathbb{P}^2$, with $epsilonin {0,1}$. Let $Gamma subset mathbb{P}^2$ be an integral curve of geometric genus $g$ and degree $m$, $Gamma neq D$, and let $nu: Cto Gamma$ be the normalization. Let $delta$ be the degree of the emph{reduction modulo 2} of the divisor $nu^*(D)$ of $C$. In this paper we prove the inequality $4g+deltageqslant m(d-8+2epsilon)+5$. We compare this with similar inequalities due to Geng Xu and Xi Chen. Besides, we provide a brief account on genera of subvarieties in projective hypersurfaces.","PeriodicalId":432671,"journal":{"name":"Functional Analysis and Geometry","volume":"29 56","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114088176","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}
引用次数: 2
On algebraically integrable bodies 代数可积体
Functional Analysis and Geometry Pub Date : 1900-01-01 DOI: 10.1090/CONM/733/14731
M. Agranovsky
{"title":"On algebraically integrable bodies","authors":"M. Agranovsky","doi":"10.1090/CONM/733/14731","DOIUrl":"https://doi.org/10.1090/CONM/733/14731","url":null,"abstract":"","PeriodicalId":432671,"journal":{"name":"Functional Analysis and Geometry","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131263810","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}
引用次数: 7
Surfaces with big automorphism groups 具有大自同构群的曲面
Functional Analysis and Geometry Pub Date : 1900-01-01 DOI: 10.1090/CONM/733/14742
S. Kaliman
{"title":"Surfaces with big automorphism groups","authors":"S. Kaliman","doi":"10.1090/CONM/733/14742","DOIUrl":"https://doi.org/10.1090/CONM/733/14742","url":null,"abstract":"","PeriodicalId":432671,"journal":{"name":"Functional Analysis and Geometry","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121854591","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}
引用次数: 1
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