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Boundary value problems of conjugate and generalized k-holomorphic functions in ℂ2 ℂ2中共轭函数和广义k-荷态函数的边界值问题
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0511-6
Yanyan Cui, Chaojun Wang, Yonghong Xie, Yuying Qiao
{"title":"Boundary value problems of conjugate and generalized k-holomorphic functions in ℂ2","authors":"Yanyan Cui, Chaojun Wang, Yonghong Xie, Yuying Qiao","doi":"10.1007/s10473-024-0511-6","DOIUrl":"https://doi.org/10.1007/s10473-024-0511-6","url":null,"abstract":"<p>In this paper, conjugate <i>k</i>-holomorphic functions and generalized <i>k</i>-holomorphic functions are defined in the two-dimensional complex space, and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders. By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate <i>k</i>-holomorphic kernels, the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion, and the integral expressions of the solutions are obtained.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"4 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195129","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 singular Dirichlet problem for the Monge-Ampère type equation Monge-Ampère 型方程的奇异 Dirichlet 问题
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0520-5
Zhijun Zhang, Bo Zhang
{"title":"A singular Dirichlet problem for the Monge-Ampère type equation","authors":"Zhijun Zhang, Bo Zhang","doi":"10.1007/s10473-024-0520-5","DOIUrl":"https://doi.org/10.1007/s10473-024-0520-5","url":null,"abstract":"<p>We consider the singular Dirichlet problem for the Monge-Ampère type equation <span>({rm det} D^2 u=b(x)g(-u)(1+|nabla u|^2)^{q/2}, u&lt;0, x in Omega, u|_{partial Omega}=0)</span>, where Ω is a strictly convex and bounded smooth domain in ℝ<sup><i>n</i></sup>, <i>q</i> ∈ [0, <i>n</i> +1), <i>g</i> ∈ <i>C</i><sup>∞</sup> (0, ∞) is positive and strictly decreasing in (0, ∞) with <span>(limlimits_{srightarrow 0^+}g(s)=infty)</span>, and <i>b</i> ∈ <i>C</i><sup>∞</sup> (Ω) is positive in Ω. We obtain the existence, nonexistence and global asymptotic behavior of the convex solution to such a problem for more general <i>b</i> and <i>g</i>. Our approach is based on the Karamata regular variation theory and the construction of suitable sub-and super-solutions.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"4 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195169","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
The Schur test of compact operators 紧凑算子的舒尔检验
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0524-1
Qijian Kang, Maofa Wang
{"title":"The Schur test of compact operators","authors":"Qijian Kang, Maofa Wang","doi":"10.1007/s10473-024-0524-1","DOIUrl":"https://doi.org/10.1007/s10473-024-0524-1","url":null,"abstract":"<p>Infinite matrix theory is an important branch of function analysis. Every linear operator on a complex separable infinite dimensional Hilbert space corresponds to an infinite matrix with respect a orthonormal base of the space, but not every infinite matrix corresponds to an operator. The classical Schur test provides an elegant and useful criterion for the boundedness of linear operators, which is considered a respectable mathematical accomplishment. In this paper, we prove the compact version of the Schur test. Moreover, we provide the Schur test for the Schatten class <i>S</i><sub>2</sub>. It is worth noting that our main results can be applicable to the general matrix without limitation on non-negative numbers. We finally provide the Schur test for compact operators from <i>l</i><sub><i>p</i></sub> into <i>l</i><sub><i>q</i></sub>.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"38 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195173","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
Lévy area analysis and parameter estimation for fOU processes via non-geometric rough path theory 通过非几何粗糙路径理论对 fOU 过程进行莱维区分析和参数估计
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0501-8
Zhongmin Qian, Xingcheng Xu
{"title":"Lévy area analysis and parameter estimation for fOU processes via non-geometric rough path theory","authors":"Zhongmin Qian, Xingcheng Xu","doi":"10.1007/s10473-024-0501-8","DOIUrl":"https://doi.org/10.1007/s10473-024-0501-8","url":null,"abstract":"<p>This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting. To tackle this problem, we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path. Our approach is particularly suitable for high-frequency data. To formulate the parameter estimators, we introduce a theory of pathwise Itô integrals with respect to fractional Brownian motion. By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes, we demonstrate that our estimators are strongly consistent and pathwise stable. Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings, and may have practical implications for fields including finance, economics, and engineering.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"168 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195121","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 operators between weighted Bergman spaces over the half-plane 半平面上加权伯格曼空间之间的托普利兹算子
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0504-5
Lixia Feng, Yan Li, Zhiyu Wang, Liankuo Zhao
{"title":"Toeplitz operators between weighted Bergman spaces over the half-plane","authors":"Lixia Feng, Yan Li, Zhiyu Wang, Liankuo Zhao","doi":"10.1007/s10473-024-0504-5","DOIUrl":"https://doi.org/10.1007/s10473-024-0504-5","url":null,"abstract":"<p>In this paper, by characterizing Carleson measures, we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békollé weights over the half-plane for all index choices.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"40 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195124","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 the Cauchy problem for the generalized Boussinesq equation with a damped term 关于带阻尼项的广义布森斯克方程的考希问题
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0508-1
Xiao Su, Shubin Wang
{"title":"On the Cauchy problem for the generalized Boussinesq equation with a damped term","authors":"Xiao Su, Shubin Wang","doi":"10.1007/s10473-024-0508-1","DOIUrl":"https://doi.org/10.1007/s10473-024-0508-1","url":null,"abstract":"<p>This paper is devoted to the Cauchy problem for the generalized damped Boussinesq equation with a nonlinear source term in the natural energy space. With the help of linear time-space estimates, we establish the local existence and uniqueness of solutions by means of the contraction mapping principle. The global existence and blow-up of the solutions at both subcritical and critical initial energy levels are obtained. Moreover, we construct the sufficient conditions of finite time blow-up of the solutions with arbitrary positive initial energy.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"10 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195126","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 compact embedding result for nonlocal Sobolev spaces and multiplicity of sign-changing solutions for nonlocal Schrödinger equations 非局部索波列夫空间的紧凑嵌入结果和非局部薛定谔方程符号变化解的多重性
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0512-5
Xu Zhang, Hao Zhai, Fukun Zhao
{"title":"A compact embedding result for nonlocal Sobolev spaces and multiplicity of sign-changing solutions for nonlocal Schrödinger equations","authors":"Xu Zhang, Hao Zhai, Fukun Zhao","doi":"10.1007/s10473-024-0512-5","DOIUrl":"https://doi.org/10.1007/s10473-024-0512-5","url":null,"abstract":"<p>For any <i>s</i> ∈ (0, 1), let the nonlocal Sobolev space <i>X</i><sup><i>s</i></sup>(ℝ<sup><i>N</i></sup>) be the linear space of Lebesgue measure functions from ℝ<sup><i>N</i></sup> to ℝ such that any function <i>u</i> in <i>X</i><sup>s</sup>(ℝ<sup><i>N</i></sup>) belongs to <i>L</i><sup>2</sup>(ℝ<sup><i>N</i></sup>) and the function</p><span>$$(x,y)longmapstobig(u(x)-u(y)big)sqrt{K(x-y)}$$</span><p>is in <i>L</i><sup>2</sup>(ℝ<sup><i>N</i></sup>, ℝ<sup><i>N</i></sup>). First, we show, for a coercive function <i>V</i>(<i>x</i>), the subspace</p><span>$$E:=bigg{uin X^s(mathbb{R}^N):int_{mathbb{R}^N}V(x)u^2{rm d}x&lt;+inftybigg}$$</span><p>of <i>X</i><sup><i>s</i></sup>(ℝ<sup><i>N</i></sup>) is embedded compactly into <i>L</i><sup><i>p</i></sup>(ℝ<sup><i>N</i></sup>) for <span>(pin[2,2_s^*))</span>, where <span>(2_s^*)</span> is the fractional Sobolev critical exponent. In terms of applications, the existence of a least energy sign-changing solution and infinitely many sign-changing solutions of the nonlocal Schrödinger equation</p><span>$$-{cal{L}_K}u+V(x)u=f(x,u), xin mathbb{R}^N$$</span><p>are obtained, where <span>(-{cal{L}_K})</span> is an integro-differential operator and <i>V</i> is coercive at infinity.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"26 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195130","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
Global convergence of a cautious projection BFGS algorithm for nonconvex problems without gradient Lipschitz continuity 针对无梯度 Lipschitz 连续性非凸问题的谨慎投影 BFGS 算法的全局收敛性
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0506-3
Gonglin Yuan, Xiong Zhao, Jiajia Yu
{"title":"Global convergence of a cautious projection BFGS algorithm for nonconvex problems without gradient Lipschitz continuity","authors":"Gonglin Yuan, Xiong Zhao, Jiajia Yu","doi":"10.1007/s10473-024-0506-3","DOIUrl":"https://doi.org/10.1007/s10473-024-0506-3","url":null,"abstract":"<p>A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems. The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption, which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method. Under some additional conditions, the method presented has a superlinear convergence rate, which can be regarded as an extension and supplement of BFGS-type methods with the projection technique. Finally, the effectiveness and application prospects of the proposed method are verified by numerical experiments.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"40 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195176","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
Variational analysis for the maximal time function in normed spaces 规范空间中最大时间函数的变量分析
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0503-6
Ziyi Zhou, Yi Jiang
{"title":"Variational analysis for the maximal time function in normed spaces","authors":"Ziyi Zhou, Yi Jiang","doi":"10.1007/s10473-024-0503-6","DOIUrl":"https://doi.org/10.1007/s10473-024-0503-6","url":null,"abstract":"<p>For a general normed vector space, a special optimal value function called a maximal time function is considered. This covers the farthest distance function as a special case, and has a close relationship with the smallest enclosing ball problem. Some properties of the maximal time function are proven, including the convexity, the lower semicontinuity, and the exact characterizations of its subdifferential formulas.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"26 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195123","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
The stable reconstruction of strongly-decaying block sparse signals 强衰减块状稀疏信号的稳定重建
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0509-0
Yifang Yang, Jinping Wang
{"title":"The stable reconstruction of strongly-decaying block sparse signals","authors":"Yifang Yang, Jinping Wang","doi":"10.1007/s10473-024-0509-0","DOIUrl":"https://doi.org/10.1007/s10473-024-0509-0","url":null,"abstract":"<p>In this paper, we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit (BgOMP) algorithm in the <i>l</i><sub>2</sub>-bounded noise case. Under some restraints on the minimum magnitude of the nonzero elements of the strongly-decaying block sparse signal, if the sensing matrix satisfies the the block restricted isometry property (block-RIP), then arbitrary strongly-decaying block sparse signals can be accurately and steadily reconstructed by the BgOMP algorithm in iterations. Furthermore, we conjecture that this condition is sharp.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"15 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195127","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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