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Kernel, Image and Scattering Representations of Passive State/Signal Systems 被动状态/信号系统的内核、图像和散射表示法
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-08-14 DOI: 10.1007/s11785-024-01581-7
Damir Z. Arov
{"title":"Kernel, Image and Scattering Representations of Passive State/Signal Systems","authors":"Damir Z. Arov","doi":"10.1007/s11785-024-01581-7","DOIUrl":"https://doi.org/10.1007/s11785-024-01581-7","url":null,"abstract":"<p>In this work the characteristic properties of image and kernel representations of passive and conservative state/signal systems are presented. Earlier these representations were introduced in joint papers with Olof J. Staffans on theory of linear state/signal systems for much wider class, namely closed state/signal systems. In the case of passive and conservative state/signal systems the central role in our theory play scattering representations instead of these representations. In this paper the connections between image and scattering representations of a passive state/signal system are established, too. Main notions and results of passive s/s theory are connected with known notions and results from Krein spaces that are intensively used here. At the end an example of passive and conservative state/signal system is demonstrate on a simple quantum graph.\u0000</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"5 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Semi-commutants of Toeplitz Operators on Fock–Sobolev Space of Nonnegative Orders 非负数阶的 Fock-Sobolev 空间上 Toeplitz 算子的半通约数
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-08-05 DOI: 10.1007/s11785-024-01574-6
Jie Qin
{"title":"Semi-commutants of Toeplitz Operators on Fock–Sobolev Space of Nonnegative Orders","authors":"Jie Qin","doi":"10.1007/s11785-024-01574-6","DOIUrl":"https://doi.org/10.1007/s11785-024-01574-6","url":null,"abstract":"<p>We make a progress towards describing the semi-commutants of Toeplitz operators on the Fock–Sobolev space of nonnegative orders. We generalize the results in Bauer et al. (J Funct Anal 268:3017, 2015) and Qin (Bull Sci Math 179:103156, 2022). For the certain symbol spaces, we obtain two Toeplitz operators can semi-commute only in the trivial case, which is different from what is known for the classical Fock space. As an application, we consider the conjecture which was shown to be false for the Fock space in Ma et al. (J Funct Anal 277:2644–2663, 2019). The main result of this paper says that there is a fundamental difference between the geometries of the Fock and Fock–Sobolev space.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"27 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Gradient Estimates in the Whole Space for the Double Phase Problems by the Maximal Function Method 用最大函数法估算双相问题整个空间的梯度
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-08-01 DOI: 10.1007/s11785-024-01579-1
Beilei Zhang, Bin Ge
{"title":"Gradient Estimates in the Whole Space for the Double Phase Problems by the Maximal Function Method","authors":"Beilei Zhang, Bin Ge","doi":"10.1007/s11785-024-01579-1","DOIUrl":"https://doi.org/10.1007/s11785-024-01579-1","url":null,"abstract":"<p>Within this article, the maximal function method is used to establish the Calderón-Zygmund estimates for the weak solutions of a class of non-uniformly elliptic equations </p><span>$$begin{aligned} -textrm{div}A(x,Du)=-textrm{div}F(x,f) quad in quad {mathbb {R}}^n, end{aligned}$$</span><p>where <span>(A(x,Du)approx |Du|^{p_1-2}+mu (x)|Du|^{p_2-2})</span>, <span>(F(x,f)approx |f|^{p_1-2}+mu (x)|f|^{p_2-2})</span> and <span>(1&lt;p_1&lt;p_2)</span>, <span>(0le mu (cdot )in C^{0,alpha }({mathbb {R}}^n),;alpha in (0,1])</span>. The aforementioned problems arise as Euler-Lagrange equations for variational functionals that were originally presented and studied within the context of Homogenization and the Lavrentiev phenomenon by Marcellini (Arch Ration Mech Anal 105:267–284, 1989. https://doi.org/10.1007/BF00251503) and Zhikov (Izv Akad Nauk SSSR Ser Mat 29:33–66, 1987. https://doi.org/10.1070/IM1987v029n01ABEH000958). They are distinctive in that they exhibit that the growth and ellipticity change between two distinct types of polynomial depending on the position. This feature is characteristic of strongly anisotropic materials. The contribution of this paper is closely tied to the significant advancements made by Colombo and Mingione (J Funct Anal 270:1416–1478, 2016. https://doi.org/10.1016/j.jfa.2015.06.022) in the qualitative analysis of double phase problems, as well as the related techniques used by Zhang et al. (Ann Polon Math, 114:45–65, 2015. https://doi.org/10.4064/ap114-1-4).</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"77 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Sharp Pointwise Estimate of $$alpha $$ -Harmonic Functions 谐函数 $$alpha $$ 的尖锐点估计
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-07-20 DOI: 10.1007/s11785-024-01578-2
David Kalaj
{"title":"Sharp Pointwise Estimate of $$alpha $$ -Harmonic Functions","authors":"David Kalaj","doi":"10.1007/s11785-024-01578-2","DOIUrl":"https://doi.org/10.1007/s11785-024-01578-2","url":null,"abstract":"<p>Let <span>(alpha &gt;-1)</span> and assume that <i>f</i> is <span>(alpha )</span>-harmonic mapping defined in the unit disk that belongs to the Hardy class <span>(h^p)</span> with <span>(pgeqslant 1)</span>. We obtain some sharp estimates of the type <span>(|f(z)|le g(|r|) Vert f^*Vert _p)</span> and <span>(|Df(z)|le h(|r|)Vert f^*Vert _p)</span>. We also prove a Schwarz type lemma for the class of <span>(alpha )</span>-harmonic mappings of the unit disk onto itself fixing the origin.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"18 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Spectral Analysis of an Operator with Fourier-Neumann Expansions Beneath 带有傅里叶-诺伊曼展开的算子的谱分析
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-07-17 DOI: 10.1007/s11785-024-01577-3
Krzysztof Stempak
{"title":"Spectral Analysis of an Operator with Fourier-Neumann Expansions Beneath","authors":"Krzysztof Stempak","doi":"10.1007/s11785-024-01577-3","DOIUrl":"https://doi.org/10.1007/s11785-024-01577-3","url":null,"abstract":"<p>We perform spectral analysis of a Sturm-Liouville operator on <span>(L^2(mathbb {R}_+,dx))</span> which, through the Liouville transformation, is unitarily equivalent to the Schrödinger operator on <span>(L^2(mathbb {R},dx))</span> with heavy negative potential <span>(V(x)=-e^{2x})</span>. This analysis clarifies some operator theory aspects of the setting of Fourier-Neumann expansions initiated by Varona in 1994. </p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"29 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141721941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Toeplitz and Hankel Operators on Vector-Valued Fock-Type Spaces 向量值福克型空间上的托普利兹和汉克尔算子
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-07-17 DOI: 10.1007/s11785-024-01575-5
Chunxu Xu, Jianxiang Dong, Tao Yu
{"title":"Toeplitz and Hankel Operators on Vector-Valued Fock-Type Spaces","authors":"Chunxu Xu, Jianxiang Dong, Tao Yu","doi":"10.1007/s11785-024-01575-5","DOIUrl":"https://doi.org/10.1007/s11785-024-01575-5","url":null,"abstract":"<p>In this paper, we study some characterizations of the Toeplitz and Hankel operators with positive operator-valued function as symbol on the vector-valued Fock-type spaces. We first discuss that the Bergman projection <span>(P:L^p_{Psi }({mathcal {H}})rightarrow F^p_{Psi }({mathcal {H}}))</span> is bounded for all <span>(1le ple infty )</span>, and obtain the duality of the vector-valued Fock-type spaces. Second, using operator-valued Carleson conditions, we give a complete characterization of the boundedness and compactness of the Toeplitz operators on <span>(F^p_{Psi }({mathcal {H}})(1&lt;p&lt;infty ))</span>. Finally, we describe the boundedness (or compactness) of the Hankel operators <span>(H_G)</span> and <span>(H_{G^*})</span> on <span>(F_{Psi }^2({mathcal {H}}))</span> in terms of a bounded (or vanishing) mean oscillation. We also give geometrical descriptions for the operator-valued spaces <span>(BMO_Psi ^2)</span> and <span>(VMO_Psi ^2)</span> defined in terms of the Berezin transform.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"36 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Clark Measures on Bounded Symmetric Domains 有界对称域上的克拉克量纲
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-07-11 DOI: 10.1007/s11785-024-01571-9
Mattia Calzi
{"title":"Clark Measures on Bounded Symmetric Domains","authors":"Mattia Calzi","doi":"10.1007/s11785-024-01571-9","DOIUrl":"https://doi.org/10.1007/s11785-024-01571-9","url":null,"abstract":"<p>Given a bounded symmetric domain <i>D</i>, we study (positive) pluriharmonic functions on <i>D</i> and investigate a possible analogue of the family of Clark measures associated with a holomorphic function from <i>D</i> into the unit disc in <span>(mathbb {C})</span>.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"95 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141611419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A Generalization of Ando’s Dilation, and Isometric Dilations for a Class of Tuples of q-Commuting Contractions 安藤扩张的一般化，以及一类 q 对等收缩元组的等距扩张
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-07-10 DOI: 10.1007/s11785-024-01551-z
Sibaprasad Barik, Bappa Bisai
{"title":"A Generalization of Ando’s Dilation, and Isometric Dilations for a Class of Tuples of q-Commuting Contractions","authors":"Sibaprasad Barik, Bappa Bisai","doi":"10.1007/s11785-024-01551-z","DOIUrl":"https://doi.org/10.1007/s11785-024-01551-z","url":null,"abstract":"<p>Given a bounded operator <i>Q</i> on a Hilbert space <span>(mathcal {H})</span>, a pair of bounded operators <span>((T_1,T_2))</span> on <span>(mathcal {H})</span> is said to be <i>Q</i>-commuting if one of the following holds: </p><span>$$begin{aligned} T_1T_2=QT_2T_1 text { or }T_1T_2=T_2QT_1 text { or }T_1T_2=T_2T_1Q. end{aligned}$$</span><p>We give an explicit construction of isometric dilations for pairs of <i>Q</i>-commuting contractions for unitary <i>Q</i>, which generalizes the isometric dilation of Ando (Acta Sci Math (Szeged) 24:88–90, 1963) for pairs of commuting contractions. In particular, for <span>(Q=qI_{mathcal {H}})</span>, where <i>q</i> is a complex number of modulus 1, this gives, as a corollary, an explicit construction of isometric dilations for pairs of <i>q</i>-commuting contractions, which are well studied. There is an extended notion of <i>q</i>-commutativity for general tuples of operators and it is known that isometric dilation does not hold, in general, for an <i>n</i>-tuple of <i>q</i>-commuting contractions, where <span>(nge 3)</span>. Generalizing the class of commuting contractions considered by Brehmer (Acta Sci Math (Szeged) 22:106–111, 1961), we construct a class of <i>n</i>-tuples of <i>q</i>-commuting contractions and find isometric dilations explicitly for the class.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"78 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141577676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Deformations and q-Convolutions. Old and New Results 变形与 q-自旋。新旧成果
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-07-07 DOI: 10.1007/s11785-024-01572-8
Marek Bożejko, Wojciech Bożejko
{"title":"Deformations and q-Convolutions. Old and New Results","authors":"Marek Bożejko, Wojciech Bożejko","doi":"10.1007/s11785-024-01572-8","DOIUrl":"https://doi.org/10.1007/s11785-024-01572-8","url":null,"abstract":"<p>This paper is the survey of some of our results related to <i>q</i>-deformations of the Fock spaces and related to <i>q</i>-convolutions for probability measures on the real line <span>(mathbb {R})</span>. The main idea is done by the combinatorics of moments of the measures and related <i>q</i>-cumulants of different types. The main and interesting <i>q</i>-convolutions are related to classical continuous (discrete) <i>q</i>-Hermite polynomial. Among them are classical (<span>(q=1)</span>) convolutions, the case <span>(q=0)</span>, gives the free and Boolean relations, and the new class of <i>q</i>-analogue of classical convolutions done by Carnovole, Koornwinder, Biane, Anshelovich, and Kula. The paper contains many questions and problems related to the positivity of that class of <i>q</i>-convolutions. The main result is the construction of Brownian motion related to <i>q</i>-Discrete Hermite polynomial of type I.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"35 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Generalized Volterra Integral Operators on Fock Spaces Fock 空间上的广义 Volterra 积分算子
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-07-05 DOI: 10.1007/s11785-024-01573-7
Yongqing Liu
{"title":"Generalized Volterra Integral Operators on Fock Spaces","authors":"Yongqing Liu","doi":"10.1007/s11785-024-01573-7","DOIUrl":"https://doi.org/10.1007/s11785-024-01573-7","url":null,"abstract":"<p>In this paper, we extend the Voleterra integral operator <span>(V_g)</span> and its companion <span>(J_g)</span> to integral operator </p><span>$$begin{aligned} T_g^{n,m}f(z)=int _0^z f^{(n)}(w) g^{(m)}(w)dw. end{aligned}$$</span><p>Using a unified approach, we completely characterize the boundedness and compactness of <span>(T_g^{n,m})</span> from one Fock space <span>(F_alpha ^p)</span> to another <span>(F_beta ^q)</span> for <span>(0&lt;p,qle infty )</span>, <span>(0&lt;alpha ,beta &lt;infty )</span>. As a surprising case, we obtain that the boundedness (compactness) of <span>(V_g)</span> and <span>(J_g)</span> from <span>(F_alpha ^p)</span> to <span>(F_beta ^q)</span> is equivalent when the weight parameter <span>(alpha &lt;beta )</span>. We also estimate the norms and essential norms of <span>(T_g^{n,m})</span>.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"53 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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