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Qualitative uncertainty principle for continuous modulated shearlet transform 连续调制小剪切变换的定性不确定性原理
IF 0.8
Advances in Operator Theory Pub Date : 2024-05-10 DOI: 10.1007/s43036-024-00346-5
Piyush Bansal, Ajay Kumar, Ashish Bansal
{"title":"Qualitative uncertainty principle for continuous modulated shearlet transform","authors":"Piyush Bansal,&nbsp;Ajay Kumar,&nbsp;Ashish Bansal","doi":"10.1007/s43036-024-00346-5","DOIUrl":"10.1007/s43036-024-00346-5","url":null,"abstract":"<div><p>We prove the qualitative uncertainty principle for the continuous modulated shearlet transform on several classes of groups including Abelian groups, compact extensions of Abelian groups and Heisenberg group. As particular cases, one obtains the qualitative uncertainty principles for the Gabor transform, the wavelet transform and the shearlet transform.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140991558","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: 0
On sum of weighted differentiation composition operators from Bergman spaces with admissible weights to Zygmund type spaces 论从具有可容许权重的伯格曼空间到齐格蒙类型空间的加权微分组成算子之和
IF 0.8
Advances in Operator Theory Pub Date : 2024-04-30 DOI: 10.1007/s43036-024-00345-6
Ajay K. Sharma, Sanjay Kumar, Mehak Sharma, Bhanu Sharma, Mohammad Mursaleen
{"title":"On sum of weighted differentiation composition operators from Bergman spaces with admissible weights to Zygmund type spaces","authors":"Ajay K. Sharma,&nbsp;Sanjay Kumar,&nbsp;Mehak Sharma,&nbsp;Bhanu Sharma,&nbsp;Mohammad Mursaleen","doi":"10.1007/s43036-024-00345-6","DOIUrl":"10.1007/s43036-024-00345-6","url":null,"abstract":"<div><p>Let <span>({mathbb D})</span> be the open unit disk in the complex plane. We characterize the boundedness and compactness of the sum of weighted differentiation composition operators </p><div><div><span>$$begin{aligned} (T_{overrightarrow{psi }, varphi } f)(z)=sum _{j=0}^{n}(D^j_{psi _j, varphi }f)(z)=sum _{j=0}^npsi _{j}(z) f^{(j)} (varphi (z)),quad zin {mathbb D}, end{aligned}$$</span></div></div><p>where <span>(nin {mathbb N}_0)</span>, <span>(psi _j)</span>, <span>(jin overline{0,n})</span>, are holomorphic functions on <span>({mathbb D})</span>, and <span>(varphi )</span>, a holomorphic self-maps of <span>({mathbb D})</span>, acting from Bergman spaces with admissible weights to Zygmund type spaces.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415029","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: 0
Extrapolation to two-weighted Herz spaces with three variable exponents 外推至具有三个可变指数的双加权赫兹空间
IF 0.8
Advances in Operator Theory Pub Date : 2024-04-29 DOI: 10.1007/s43036-024-00333-w
Mitsuo Izuki, Takahiro Noi, Yoshihiro Sawano
{"title":"Extrapolation to two-weighted Herz spaces with three variable exponents","authors":"Mitsuo Izuki,&nbsp;Takahiro Noi,&nbsp;Yoshihiro Sawano","doi":"10.1007/s43036-024-00333-w","DOIUrl":"10.1007/s43036-024-00333-w","url":null,"abstract":"<div><p>On the basis of the boundedness of singular integral operators, we investigate the boundedness of various linear operators acting on two-weighted Herz spaces with three variable exponents. We obtain the extrapolation theorem as well as the boundedness property of bilinear singular operators. First, we are interested in the case where the triangle inequality is available, and then we develop a theory to extend our results in full generality.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414780","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: 0
Birkhoff–James classification of norm’s properties 规范特性的伯克霍夫-詹姆斯分类法
IF 0.8
Advances in Operator Theory Pub Date : 2024-04-26 DOI: 10.1007/s43036-024-00321-0
Alexander Guterman, Bojan Kuzma, Sushil Singla, Svetlana Zhilina
{"title":"Birkhoff–James classification of norm’s properties","authors":"Alexander Guterman,&nbsp;Bojan Kuzma,&nbsp;Sushil Singla,&nbsp;Svetlana Zhilina","doi":"10.1007/s43036-024-00321-0","DOIUrl":"10.1007/s43036-024-00321-0","url":null,"abstract":"<div><p>For an arbitrary normed space <span>(mathcal {X})</span> over a field <span>(mathbb {F}in { mathbb {R}, mathbb {C}},)</span> we define the directed graph <span>(Gamma (mathcal {X}))</span> induced by Birkhoff–James orthogonality on the projective space <span>(mathbb P(mathcal {X}),)</span> and also its nonprojective counterpart <span>(Gamma _0(mathcal {X}).)</span> We show that, in finite-dimensional normed spaces, <span>(Gamma (mathcal {X}))</span> carries all the information about the dimension, smooth points, and norm’s maximal faces. It also allows to determine whether the norm is a supremum norm or not, and thus classifies finite-dimensional abelian <span>(C^*)</span>-algebras among other normed spaces. We further establish the necessary and sufficient conditions under which the graph <span>(Gamma _0({mathcal {R}}))</span> of a (real or complex) Radon plane <span>({mathcal {R}})</span> is isomorphic to the graph <span>(Gamma _0(mathbb {F}^2, {Vert cdot Vert }_2))</span> of the two-dimensional Hilbert space and construct examples of such nonsmooth Radon planes.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00321-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Daugavet’s equation and Jordan elementary operators 道加韦特方程和约旦基本算子
IF 0.8
Advances in Operator Theory Pub Date : 2024-04-24 DOI: 10.1007/s43036-024-00342-9
Zakaria Taki, Mohamed Chraibi Kaadoud, Messaoud Guesba
{"title":"Daugavet’s equation and Jordan elementary operators","authors":"Zakaria Taki,&nbsp;Mohamed Chraibi Kaadoud,&nbsp;Messaoud Guesba","doi":"10.1007/s43036-024-00342-9","DOIUrl":"10.1007/s43036-024-00342-9","url":null,"abstract":"<div><p>The aim of this paper is to investigate the Daugavet equation for a Jordan elementary operator. More precisely, we study the equation </p><div><div><span>$$begin{aligned} Vert I+U_{mathfrak {J},A,B} Vert =1+2 Vert A Vert Vert B Vert , end{aligned}$$</span></div></div><p>where <i>I</i> stands for the identity operator, <i>A</i> and <i>B</i> are two bounded operators acting on a complex Hilbert space <span>(mathcal {H})</span>, <span>(mathfrak {J})</span> is a norm ideal of operators on <span>(mathcal {H})</span>, and <span>(U_{mathfrak {J}, A, B})</span> is the restriction of the Jordan operator <span>(U_{A,B})</span> to <span>(mathfrak {J})</span>. In the particular case where <span>(mathfrak {J}=mathfrak {C}_{2}(mathcal {H}))</span> is the ideal of Hilbert–Schmidt operators, we give necessary and sufficient conditions under which the above equation holds.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140665024","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: 0
Mosco convergence of set-valued supermartingale 集合值超马太尔的莫斯科收敛性
IF 0.8
Advances in Operator Theory Pub Date : 2024-04-23 DOI: 10.1007/s43036-024-00340-x
M’hamed El-Louh, Fatima Ezzaki
{"title":"Mosco convergence of set-valued supermartingale","authors":"M’hamed El-Louh,&nbsp;Fatima Ezzaki","doi":"10.1007/s43036-024-00340-x","DOIUrl":"10.1007/s43036-024-00340-x","url":null,"abstract":"<div><p>The existence of regular martingale selectors for multivalued supermartingales with unbounded values in a separable Banach space <i>Y</i> is proved. In addition, new convergence results for set-valued supermartingales in the Mosco sense are presented. At the end of this paper, the equivalence between some properties of unbounded set-valued supermartingales and the convergence of these random sets in the Mosco sense is established.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140671285","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: 0
On the generalized n-strong Drazin inverses and block matrices in Banach algebras 论巴拿赫数组中的广义 n 强 Drazin 逆和块矩阵
IF 0.8
Advances in Operator Theory Pub Date : 2024-04-21 DOI: 10.1007/s43036-024-00341-w
Othman Abad, Aymen Bahloul
{"title":"On the generalized n-strong Drazin inverses and block matrices in Banach algebras","authors":"Othman Abad,&nbsp;Aymen Bahloul","doi":"10.1007/s43036-024-00341-w","DOIUrl":"10.1007/s43036-024-00341-w","url":null,"abstract":"<div><p>Let <span>(mathcal {A})</span> be a complex unital Banach algebra. The purpose of this paper is to give a new characterization of generalized <i>n</i>-strong Drazin invertible elements by means of their spectra. Consequently, we address key results in relation with the problem of existence and representations of the generalized <i>n</i>-strong Drazin inverse of the block matrix <span>(x=left( begin{array}{cc}a&amp;{}b c&amp;{}dend{array}right) _{p})</span> relative to the idempotent <i>p</i>, with <i>a</i> is generalized Drazin invertible such that <span>(a^{d})</span> is its generalized Drazin inverse in <span>(p mathcal {A}p)</span>, under the more general case of the generalized Schur complement <span>(s=d-ca^{d}b)</span> being generalized Drazin invertible.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140678805","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: 0
On power series subspaces of certain nuclear Fréchet spaces 论某些核弗雷谢特空间的幂级数子空间
IF 0.8
Advances in Operator Theory Pub Date : 2024-04-15 DOI: 10.1007/s43036-024-00335-8
Nazlı Doğan
{"title":"On power series subspaces of certain nuclear Fréchet spaces","authors":"Nazlı Doğan","doi":"10.1007/s43036-024-00335-8","DOIUrl":"10.1007/s43036-024-00335-8","url":null,"abstract":"<div><p>The diametral dimension, <span>(Delta (E),)</span> and the approximate diametral dimension, <span>(delta (E))</span> of an element <i>E</i> of a class of nuclear Fréchet spaces, which satisfies <span>((underline{DN}))</span> and <span>(Omega )</span> are set theoretically between the respective invariant of power series spaces <span>(Lambda _{1}(varepsilon ))</span> and <span>(Lambda _{infty }(varepsilon ))</span> for some exponent sequence <span>(varepsilon .)</span> Aytuna et al. (Manuscr Math 67:125–142, 1990) proved that <i>E</i> contains a complemented subspace which is isomorphic to <span>(Lambda _{infty }(varepsilon ))</span> provided <span>(Delta (E)= Lambda _{infty }^{prime }(varepsilon )))</span> and <span>(varepsilon )</span> is stable. In this article, we consider the other extreme case and we prove that, there exist nuclear Fréchet spaces with the properties <span>((underline{DN}))</span> and <span>(Omega ,)</span> even regular nuclear Köthe spaces, satisfying <span>(Delta (E)=Lambda _{1}(varepsilon ))</span> such that there is no subspace of <i>E</i> which is isomorphic to <span>(Lambda _{1}(varepsilon ).)</span></p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140795928","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: 0
Cotlar-type inequality and weighted boundedness for maximal multilinear singular integrals in Dunkl setting Dunkl 设置中最大多线性奇异积分的 Cotlar 型不等式和加权有界性
IF 0.8
Advances in Operator Theory Pub Date : 2024-04-12 DOI: 10.1007/s43036-024-00338-5
Suman Mukherjee
{"title":"Cotlar-type inequality and weighted boundedness for maximal multilinear singular integrals in Dunkl setting","authors":"Suman Mukherjee","doi":"10.1007/s43036-024-00338-5","DOIUrl":"10.1007/s43036-024-00338-5","url":null,"abstract":"<div><p>In this article, we establish a multilinear Cotlar-type inequality for the maximal multilinear singular integrals in Dunkl setting whose kernels possess less regularity conditions compared to the multilinear Calderón–Zygmund kernels in spaces of homogeneous type. As applications, we achieve weighted boundedness of maximal multilinear Dunkl–Calderón–Zygmund singular integrals and pointwise convergence of principal value integrals associated with multilinear Dunkl–Calderón–Zygmund kernels.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140783406","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: 0
Data approximation in twisted shift-invariant spaces 扭曲移变空间中的数据逼近
IF 0.8
Advances in Operator Theory Pub Date : 2024-04-11 DOI: 10.1007/s43036-024-00336-7
Radha Ramakrishnan, Rabeetha Velsamy
{"title":"Data approximation in twisted shift-invariant spaces","authors":"Radha Ramakrishnan,&nbsp;Rabeetha Velsamy","doi":"10.1007/s43036-024-00336-7","DOIUrl":"10.1007/s43036-024-00336-7","url":null,"abstract":"<div><p>Twisted convolution is a non-standard convolution which arises while transferring the convolution of the Heisenberg group to the complex plane. Under this operation of twisted convolution, <span>(L^{1}(mathbb {R}^{2n}))</span> turns out to be a non-commutative Banach algebra. Hence the study of (twisted) shift-invariant spaces on <span>(mathbb {R}^{2n})</span> completely differs from the perspective of the usual shift-invariant spaces on <span>(mathbb {R}^{d})</span>. In this paper, by considering a set of functional data <span>(mathcal {F}={f_{1},ldots ,f_{m}})</span> in <span>(L^{2}(mathbb {R}^{2n}))</span>, we construct a finitely generated twisted shift-invariant space <span>(V^{t})</span> on <span>(mathbb {R}^{2n})</span> in such a way that the corresponding system of twisted translates of generators form a Parseval frame sequence and show that it gives the best approximation for a given data, in the sense of least square error. We also find the error of approximation of <span>(mathcal {F})</span> by <span>(V^{t})</span>. Finally, we illustrate this theory with an example.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140792954","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: 0
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