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Integral Equations and Operator Theory最新文献

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Ideal Structure of Nica-Toeplitz Algebras Nica-Toeplitz 算法的理想结构
IF 0.8 3区 数学
Integral Equations and Operator Theory Pub Date : 2024-03-27 DOI: 10.1007/s00020-024-02761-y
Boris Bilich
{"title":"Ideal Structure of Nica-Toeplitz Algebras","authors":"Boris Bilich","doi":"10.1007/s00020-024-02761-y","DOIUrl":"https://doi.org/10.1007/s00020-024-02761-y","url":null,"abstract":"<p>We study the gauge-invariant ideal structure of the Nica-Toeplitz algebra <span>(mathcal {N}mathcal {T}(X))</span> of a product system (<i>A</i>, <i>X</i>) over <span>(mathbb {N}^n)</span>. We obtain a clear description of <i>X</i>-invariant ideals in <i>A</i>, that is, restrictions of gauge-invariant ideals in <span>(mathcal {Nhspace{-1.111pt}T}(X))</span> to <i>A</i>. The main result is a classification of gauge-invariant ideals in <span>(mathcal {Nhspace{-1.111pt}T}(X))</span> for a proper product system in terms of families of ideals in <i>A</i>. We also apply our results to higher-rank graphs.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"139 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140314909","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
Recovering the Shape of an Equilateral Quantum Tree by Two Spectra 通过两个光谱恢复等边量子树的形状
IF 0.8 3区 数学
Integral Equations and Operator Theory Pub Date : 2024-03-27 DOI: 10.1007/s00020-024-02759-6
Vyacheslav Pivovarchik
{"title":"Recovering the Shape of an Equilateral Quantum Tree by Two Spectra","authors":"Vyacheslav Pivovarchik","doi":"10.1007/s00020-024-02759-6","DOIUrl":"https://doi.org/10.1007/s00020-024-02759-6","url":null,"abstract":"<p>We show how to find the shape of an equilateral tree using the spectra of the Neumann and the Dirichlet problems generated by the Sturm–Liouville equation. In case of snowflake trees the spectra of the Neumann and Dirichlet problems uniquely determine the shape of the tree.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"2010 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140314929","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
In Memoriam Heinz Langer (08.08.1935-25.01.2024) 纪念海因茨-朗格（1935 年 8 月 8 日-2024 年 1 月 25 日）
IF 0.8 3区 数学
Integral Equations and Operator Theory Pub Date : 2024-03-23 DOI: 10.1007/s00020-024-02763-w
C. Tretter
{"title":"In Memoriam Heinz Langer (08.08.1935-25.01.2024)","authors":"C. Tretter","doi":"10.1007/s00020-024-02763-w","DOIUrl":"https://doi.org/10.1007/s00020-024-02763-w","url":null,"abstract":"","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"121 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198327","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 Operator Valued Haar Unitaries and Bipolar Decompositions of R-diagonal Elements 论R对角元素的算子值哈尔单元和双极分解
IF 0.8 3区 数学
Integral Equations and Operator Theory Pub Date : 2024-02-26 DOI: 10.1007/s00020-024-02760-z
{"title":"On Operator Valued Haar Unitaries and Bipolar Decompositions of R-diagonal Elements","authors":"","doi":"10.1007/s00020-024-02760-z","DOIUrl":"https://doi.org/10.1007/s00020-024-02760-z","url":null,"abstract":"<h3>Abstract</h3> <p>In the context of operator valued W<span> <span>(^*)</span> </span>-free probability theory, we study Haar unitaries, R-diagonal elements and circular elements. Several classes of Haar unitaries are differentiated from each other. The term bipolar decomposition is used for the expression of an element as <em>vx</em> where <em>x</em> is self-adjoint and <em>v</em> is a partial isometry, and we study such decompositions of operator valued R-diagonal and circular elements that are free, meaning that <em>v</em> and <em>x</em> are <span> <span>(*)</span> </span>-free from each other. In particular, we prove, when <span> <span>(B={textbf{C}}^2)</span> </span>, that if a <em>B</em>-valued circular element has a free bipolar decomposition with <em>v</em> unitary, then it has one where <em>v</em> normalizes <em>B</em>.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"2015 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139969476","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
Regular Functions on the Scaled Hypercomplex Numbers 标度超复数上的正则函数
IF 0.8 3区 数学
Integral Equations and Operator Theory Pub Date : 2024-02-26 DOI: 10.1007/s00020-024-02756-9
Daniel Alpay, Ilwoo Cho
{"title":"Regular Functions on the Scaled Hypercomplex Numbers","authors":"Daniel Alpay, Ilwoo Cho","doi":"10.1007/s00020-024-02756-9","DOIUrl":"https://doi.org/10.1007/s00020-024-02756-9","url":null,"abstract":"<p>In this paper, we study the regularity of <span>(mathbb {R})</span>-differentiable functions on open connected subsets of the scaled hypercomplex numbers <span>(left{ mathbb {H}_{t}right} _{tin mathbb {R}})</span> by studying the kernels of suitable differential operators <span>(left{ nabla _{t}right} _{tin mathbb {R}})</span>, up to scales in the real field <span>(mathbb {R})</span>.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"40 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139969471","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
Invertibility Criteria for the Biharmonic Single-Layer Potential 双谐波单层势的不可逆性标准
IF 0.8 3区 数学
Integral Equations and Operator Theory Pub Date : 2024-02-22 DOI: 10.1007/s00020-024-02758-7
{"title":"Invertibility Criteria for the Biharmonic Single-Layer Potential","authors":"","doi":"10.1007/s00020-024-02758-7","DOIUrl":"https://doi.org/10.1007/s00020-024-02758-7","url":null,"abstract":"<h3>Abstract</h3> <p>While the single-layer operator for the Laplacian is well understood, questions remain concerning the single-layer operator for the Bilaplacian, particularly with regard to invertibility issues linked with degenerate scales. In this article, we provide simple sufficient conditions ensuring this invertibility for a wide range of problems.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"13 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139955454","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 Rate of Convergence for Universality Limits 论普遍性极限的收敛率
IF 0.8 3区 数学
Integral Equations and Operator Theory Pub Date : 2024-02-21 DOI: 10.1007/s00020-024-02757-8
Roman Bessonov
{"title":"On Rate of Convergence for Universality Limits","authors":"Roman Bessonov","doi":"10.1007/s00020-024-02757-8","DOIUrl":"https://doi.org/10.1007/s00020-024-02757-8","url":null,"abstract":"<p>Given a probability measure <span>(mu )</span> on the unit circle <span>({mathbb {T}})</span>, consider the reproducing kernel <span>(k_{mu ,n}(z_1, z_2))</span> in the space of polynomials of degree at most <span>(n-1)</span> with the <span>(L^2(mu ))</span>–inner product. Let <span>(u, v in {mathbb {C}})</span>. It is known that under mild assumptions on <span>(mu )</span> near <span>(zeta in mathbb {T})</span>, the ratio <span>(k_{mu ,n}(zeta e^{u/n}, zeta e^{v/n})/k_{mu ,n}(zeta , zeta ))</span> converges to a universal limit <i>S</i>(<i>u</i>, <i>v</i>) as <span>(n rightarrow infty )</span>. We give an estimate for the rate of this convergence for measures <span>(mu )</span> with finite logarithmic integral.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139926509","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
Discussing Semigroup Bounds with Resolvent Estimates 用残差估计讨论半群界限
IF 0.8 3区 数学
Integral Equations and Operator Theory Pub Date : 2024-02-16 DOI: 10.1007/s00020-024-02754-x
Bernard Helffer, Johannes Sjöstrand, Joe Viola
{"title":"Discussing Semigroup Bounds with Resolvent Estimates","authors":"Bernard Helffer, Johannes Sjöstrand, Joe Viola","doi":"10.1007/s00020-024-02754-x","DOIUrl":"https://doi.org/10.1007/s00020-024-02754-x","url":null,"abstract":"<p>The purpose of this paper is to revisit the proof of the Gearhardt–Prüss–Huang–Greiner theorem for a semigroup <i>S</i>(<i>t</i>), following the general idea of the proofs that we have seen in the literature and to get an explicit estimate on the operator norm of <i>S</i>(<i>t</i>) in terms of bounds on the resolvent of the generator. In Helffer and Sjöstrand (From resolvent bounds to semigroup bounds. ArXiv:1001.4171v1, math. FA, 2010) by the first two authors, this was done and some applications in semiclassical analysis were given. Some of these results have been subsequently published in three books written by the two first authors Helffer (Spectral theory and its applications. Cambridge University Press, Cambridge, 2013) and Sjöstrand (Lecture notes : Spectral properties of non-self-adjoint operators. Journées équations aux dérivées partielles (2009), article no. 1), (Non self-adjoint differential operators, spectral asymptotics and random perturbations. Pseudo-differential Operators and Applications, Birkhäuser (2018)). A second work Helffer and Sjöstrand (Integral Equ Oper Theory 93(3), 2021) presents new improvements partially motivated by a paper of Wei (Sci China Math 64:507–518, 2021). In this third paper, we continue the discussion on whether the aforementioned results are optimal, and whether one can improve these results through iteration. Numerical computations will illustrate some of the abstract results.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"99 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139755388","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 Real and Imaginary Parts of Powers of the Volterra Operator 论 Volterra 算子幂的实部和虚部
IF 0.8 3区 数学
Integral Equations and Operator Theory Pub Date : 2024-02-15 DOI: 10.1007/s00020-024-02755-w
Thomas Ransford, Dashdondog Tsedenbayar
{"title":"On the Real and Imaginary Parts of Powers of the Volterra Operator","authors":"Thomas Ransford, Dashdondog Tsedenbayar","doi":"10.1007/s00020-024-02755-w","DOIUrl":"https://doi.org/10.1007/s00020-024-02755-w","url":null,"abstract":"<p>We study the real and imaginary parts of the powers of the Volterra operator on <span>(L^2[0,1])</span>, specifically their eigenvalues, their norms and their numerical ranges.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"91 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139755157","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
Regular Ideals, Ideal Intersections, and Quotients 正则表达式、理想交集和对数
IF 0.8 3区 数学
Integral Equations and Operator Theory Pub Date : 2024-01-29 DOI: 10.1007/s00020-023-02753-4
Jonathan H. Brown, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff
{"title":"Regular Ideals, Ideal Intersections, and Quotients","authors":"Jonathan H. Brown, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff","doi":"10.1007/s00020-023-02753-4","DOIUrl":"https://doi.org/10.1007/s00020-023-02753-4","url":null,"abstract":"<p>Let <span>(B subseteq A)</span> be an inclusion of <span>(C^*)</span>-algebras. We study the relationship between the regular ideals of <i>B</i> and regular ideals of <i>A</i>. We show that if <span>(B subseteq A)</span> is a regular <span>(C^*)</span>-inclusion and there is a faithful invariant conditional expectation from <i>A</i> onto <i>B</i>, then there is an isomorphism between the lattice of regular ideals of <i>A</i> and invariant regular ideals of <i>B</i>. We study properties of inclusions preserved under quotients by regular ideals. This includes showing that if <span>(D subseteq A)</span> is a Cartan inclusion and <i>J</i> is a regular ideal in <i>A</i>, then <span>(D/(Jcap D))</span> is a Cartan subalgebra of <i>A</i>/<i>J</i>. We provide a description of regular ideals in the reduced crossed product of a C<span>(^*)</span>-algebra by a discrete group.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"32 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139646531","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
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