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The Truncated Moment Problem on Reducible Cubic Curves I: Parabolic and Circular Type Relations 可还原立方曲线上的截断矩问题 I：抛物线与圆型关系
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-06-08 DOI: 10.1007/s11785-024-01554-w
Seonguk Yoo, Aljaž Zalar
{"title":"The Truncated Moment Problem on Reducible Cubic Curves I: Parabolic and Circular Type Relations","authors":"Seonguk Yoo, Aljaž Zalar","doi":"10.1007/s11785-024-01554-w","DOIUrl":"https://doi.org/10.1007/s11785-024-01554-w","url":null,"abstract":"<p>In this article we study the bivariate truncated moment problem (TMP) of degree 2<i>k</i> on reducible cubic curves. First we show that every such TMP is equivalent after applying an affine linear transformation to one of 8 canonical forms of the curve. The case of the union of three parallel lines was solved in Zalar (Linear Algebra Appl 649:186–239, 2022. https://doi.org/10.1016/j.laa.2022.05.008), while the degree 6 cases in Yoo (Integral Equ Oper Theory 88:45–63, 2017). Second we characterize in terms of concrete numerical conditions the existence of the solution to the TMP on two of the remaining cases concretely, i.e., a union of a line and a circle <span>(y(ay+x^2+y^2)=0, ain {mathbb {R}}{setminus } {0})</span>, and a union of a line and a parabola <span>(y(x-y^2)=0)</span>. In both cases we also determine the number of atoms in a minimal representing measure.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530391","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
Backtracking New Q-Newton’s Method, Newton’s Flow, Voronoi’s Diagram and Stochastic Root Finding 回溯新 Q 牛顿法、牛顿流、沃罗诺图和随机寻根
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-06-08 DOI: 10.1007/s11785-024-01558-6
John Erik Fornæss, Mi Hu, Tuyen Trung Truong, Takayuki Watanabe
{"title":"Backtracking New Q-Newton’s Method, Newton’s Flow, Voronoi’s Diagram and Stochastic Root Finding","authors":"John Erik Fornæss, Mi Hu, Tuyen Trung Truong, Takayuki Watanabe","doi":"10.1007/s11785-024-01558-6","DOIUrl":"https://doi.org/10.1007/s11785-024-01558-6","url":null,"abstract":"<p>A new variant of Newton’s method - named Backtracking New Q-Newton’s method (BNQN) - which has strong theoretical guarantee, is easy to implement, and has good experimental performance, was recently introduced by the third author. Experiments performed previously showed some remarkable properties of the basins of attractions for finding roots of polynomials and meromorphic functions, with BNQN. In general, they look more smooth than that of Newton’s method. In this paper, we continue to experimentally explore in depth this remarkable phenomenon, and connect BNQN to Newton’s flow and Voronoi’s diagram. This link poses a couple of challenging puzzles to be explained. Experiments also indicate that BNQN is more robust against random perturbations than Newton’s method and Random Relaxed Newton’s method.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"13 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512429","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
Infinite Order Differential Operators Associated with Superoscillations in the Half-Plane Barrier 半平面屏障中与超振荡相关的无穷阶微分算子
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-06-06 DOI: 10.1007/s11785-024-01549-7
Peter Schlosser
{"title":"Infinite Order Differential Operators Associated with Superoscillations in the Half-Plane Barrier","authors":"Peter Schlosser","doi":"10.1007/s11785-024-01549-7","DOIUrl":"https://doi.org/10.1007/s11785-024-01549-7","url":null,"abstract":"<p>Superoscillations are a phenomenon in physics, where linear combinations of low-frequency plane waves interfere almost destructively in such a way that the resulting wave has a higher frequency than any of the individual waves. The evolution of superoscillatory initial datum under the time dependent Schrödinger equation is stable in free space, but in general it is unclear whether it can be preserved in the presence of an external potential. In this paper, we consider the two-dimensional problem of superoscillations interacting with a half-plane barrier, where homogeneous Dirichlet or Neumann boundary conditions are imposed on the negative <span>(x_2)</span>-semiaxis. We use the Fresnel integral technique to write the wave function as an absolute convergent Green’s function integral. Moreover, we introduce the propagator of the Schrödinger equation in form of an infinite order differential operator, acting continuously on the function space of exponentially bounded entire functions. In particular, this operator allows to prove that the property of superoscillations is preserved in the form of a similar phenomenon called supershift, which is stable over time.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"112 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512430","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
On Generalized Fredholm Operators in a Right Quaternionic Hilbert Space 论右四元希尔伯特空间中的广义弗雷德霍尔姆算子
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-06-03 DOI: 10.1007/s11785-024-01553-x
Monia Boudhief
{"title":"On Generalized Fredholm Operators in a Right Quaternionic Hilbert Space","authors":"Monia Boudhief","doi":"10.1007/s11785-024-01553-x","DOIUrl":"https://doi.org/10.1007/s11785-024-01553-x","url":null,"abstract":"<p>The purpose of this paper, is to study and investigate a larger class of operators than the Fredholm ones, is the so-called, generalized Fredholm operators, in a right quaternionic separable Hilbert space with a left multiplication defined on it. More explicitly, we first prove some auxiliary results , in the quaternionic setting, that are needed in the development of this paper. After that, we prove that some special classes of operators are generalized Fredholm ones, and we establish a characterization of the generalized Fredholm operators in a specific quotient algebra. The obtained results leads to the study of the invariance of the generalized Fredholm S-spectrum of a bounded right linear operator defined on a right quaternionic separable Hilbert space under a finite-rank commuting operator.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255534","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 Projections and Paley–Wiener Theorem for the Unit Ball in $$mathbb {C}^{n}$$ $$mathbb {C}^{n}$ 中单位球的谱投影和帕利-维纳定理
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-06-03 DOI: 10.1007/s11785-024-01555-9
Noureddine Imesmad
{"title":"Spectral Projections and Paley–Wiener Theorem for the Unit Ball in $$mathbb {C}^{n}$$","authors":"Noureddine Imesmad","doi":"10.1007/s11785-024-01555-9","DOIUrl":"https://doi.org/10.1007/s11785-024-01555-9","url":null,"abstract":"<p>For <span>(nu in mathbb {R})</span>, we consider the invariant Laplacians <span>(Delta _{nu })</span> in the unit complex ball <span>({mathcal {B}}^{n}=(SU(n,1)/S(U(n)times U(1)))</span></p><span>$$begin{aligned} Delta _{nu }= &amp; {} 4(1-|z|^{2})Bigg {sum _{i,j=1}^{n}(delta _{ij}-z_{i}bar{z_{j}})dfrac{partial ^{2}}{partial z_{i}partial bar{z_{j}}}-frac{nu }{2}sum _{j=1}^{n}z_{j}dfrac{partial }{partial z_{j}}+frac{nu }{2}sum _{j=1}^{n}bar{z_{j}}dfrac{partial }{partial bar{z_{j}}}+frac{nu ^2}{4}Bigg } end{aligned}$$</span><p>and the spectral projectors <span>({mathcal {Q}}_{lambda ,nu })</span> associated to <span>(Delta _{nu })</span> defined by </p><span>$$begin{aligned} {mathcal {Q}}_{lambda ,nu }f= &amp; {} |{textbf{c}}_{nu }(lambda )|^{-2}f*varphi _{lambda ,nu }(z), end{aligned}$$</span><p>where <span>(varphi _{lambda ,nu })</span> is the <span>(S(U(n)times U(1)))</span>-invariant eigenfunction of <span>(Delta _{nu })</span> and <span>({textbf{c}}_{nu }(lambda ))</span> the Harish-Chandra function. The goal of this paper is to give an image characterization of <span>({mathcal {Q}}_{lambda ,nu })</span> of <span>({mathcal {C}}_{c}^{infty }({mathcal {B}}^{n}))</span> and <span>(L^{2}({mathcal {B}}^{n},(1-|z|^2)^{-n-1}dm(z)))</span>.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"43 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Realization of Inverse Stieltjes Functions $$(-m_alpha (z))$$ by Schrödinger L-Systems 用薛定谔 L 系统实现逆斯蒂尔杰斯函数 $$(-m_alpha (z))$$
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-30 DOI: 10.1007/s11785-024-01522-4
S. Belyi, E. Tsekanovskiĭ
{"title":"Realization of Inverse Stieltjes Functions $$(-m_alpha (z))$$ by Schrödinger L-Systems","authors":"S. Belyi, E. Tsekanovskiĭ","doi":"10.1007/s11785-024-01522-4","DOIUrl":"https://doi.org/10.1007/s11785-024-01522-4","url":null,"abstract":"<p>We study L-system realizations generated by the original Weyl–Titchmarsh functions <span>(m_alpha (z))</span>. In the case when the minimal symmetric Schrödinger operator is non-negative, we describe Schrödinger L-systems that realize inverse Stieltjes functions <span>((-m_alpha (z)))</span>. This approach allows to derive a necessary and sufficient conditions for the functions <span>((-m_alpha (z)))</span> to be inverse Stieltjes. In particular, the criteria when <span>((-m_infty (z)))</span> is an inverse Stieltjes function is provided. Moreover, it is shown that the knowledge of the value <span>(m_infty (-0))</span> and parameter <span>(alpha )</span> allows us to describe the geometric structure of the L-system realizing <span>((-m_alpha (z)))</span>. Additionally, we present the conditions in terms of the parameter <span>(alpha )</span> when the main and associated operators of a realizing <span>((-m_alpha (z)))</span> L-system have the same or different angle of sectoriality which sets connections with the Kato problem on sectorial extensions of sectorial forms. An example that illustrates the obtained results is presented in the end of the paper.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"44 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141198002","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
On Recovering Dirac Operators with Two Delays 关于恢复有两个延迟的狄拉克算子
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-29 DOI: 10.1007/s11785-024-01543-z
Biljana Vojvodić, Nebojša Djurić, Vladimir Vladičić
{"title":"On Recovering Dirac Operators with Two Delays","authors":"Biljana Vojvodić, Nebojša Djurić, Vladimir Vladičić","doi":"10.1007/s11785-024-01543-z","DOIUrl":"https://doi.org/10.1007/s11785-024-01543-z","url":null,"abstract":"<p>We study the inverse spectral problems of recovering Dirac-type functional-differential operator with two constant delays <span>(a_1)</span> and <span>(a_2)</span> not less than one-third of the length the interval. It has been proved that the operator can be recovered uniquely from four spectra when <span>(2a_1+frac{a_2}{2})</span> is not less than the length of the interval, while it is not possible otherwise.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"237 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190985","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 Polydiscs Associated to Product Functions and Multiplicative Embeddings 与积函数和乘法嵌入相关的多圆盘上的克拉克量纲
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-21 DOI: 10.1007/s11785-024-01547-9
Nell P. Jacobsson
{"title":"Clark Measures on Polydiscs Associated to Product Functions and Multiplicative Embeddings","authors":"Nell P. Jacobsson","doi":"10.1007/s11785-024-01547-9","DOIUrl":"https://doi.org/10.1007/s11785-024-01547-9","url":null,"abstract":"<p>We study Clark measures on the unit polydisc, giving an overview of recent research and investigating the Clark measures of some new examples of multivariate inner functions. In particular, we study the relationship between Clark measures and multiplication; first by introducing compositions of inner functions and multiplicative embeddings, and then by studying products of one-variable inner functions.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"57 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150145","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
Rate of Convergence for Double Rational Fourier Series 双有理傅里叶级数的收敛率
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-18 DOI: 10.1007/s11785-023-01479-w
Hardeepbhai J. Khachar, Rajendra G. Vyas
{"title":"Rate of Convergence for Double Rational Fourier Series","authors":"Hardeepbhai J. Khachar, Rajendra G. Vyas","doi":"10.1007/s11785-023-01479-w","DOIUrl":"https://doi.org/10.1007/s11785-023-01479-w","url":null,"abstract":"<p>We calculate the rate of convergence of the double rational Fourier series for regular, bounded, measurable, and two-variable functions. The rectangular oscillation of the two-variable function is used to quantify this rate. Additionally, we give an approximation of convergence rate of the double rational Fourier series for continuous functions with generalized bounded variation.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"50 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059352","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
Semicommutators of Truncated Toeplitz Operators 截断托普利兹算子的半互调器
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-13 DOI: 10.1007/s11785-024-01540-2
Xi Zhao, Tao Yu
{"title":"Semicommutators of Truncated Toeplitz Operators","authors":"Xi Zhao, Tao Yu","doi":"10.1007/s11785-024-01540-2","DOIUrl":"https://doi.org/10.1007/s11785-024-01540-2","url":null,"abstract":"<p>In this paper semicommutators of truncated Toeplitz operators on some model space are discussed. We investigate when the product or the semicommutator of two truncated Toeplitz operators is zero, respectively. We also obtain a necessary and sufficient condition for the semicommutator of two truncated Toeplitz operators to be compact.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"191 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939101","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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