加速邻近梯度算法是求解张量补全问题的经典方法之一,但将该算法应用到Hankel结构张量补全时,无法保证补全的张量能够保持Hankel结构。因此,本文基于加速邻近梯度算法的框架,提出了一种保Hankel结构的加速邻近梯度算法。该算法在每次迭...加速邻近梯度算法是求解张量补全问题的经典方法之一,但将该算法应用到Hankel结构张量补全时,无法保证补全的张量能够保持Hankel结构。因此,本文基于加速邻近梯度算法的框架,提出了一种保Hankel结构的加速邻近梯度算法。该算法在每次迭代中利用l∞-模投影算子生成Hankel结构张量。在理论上,本文证明了新算法在合理假设条件下的收敛性。最后,通过随机Hankel张量补全与图像修复实例的数值实验验证了新算法的有效性。The accelerated proximal gradient algorithm is one of the classic methods for solving tensor completion problems. However, when applied to Hankel structured tensor completion, it cannot guarantee that the completed tensor can maintain the Hankel structure. Therefore, based on the framework of the accelerated proximal gradient algorithm, this paper proposes a new accelerated proximal gradient algorithm that can preserve the Hankel structure. In each iteration of the algorithm, utilizing the l∞-norm projection and the fast singular value thresholding method ensures that the generated tensor preserves the Hankel structure. Moreover, this paper proves the convergence of the new algorithm under reasonable assumptions. Finally, the effectiveness of the new algorithm is verified through numerical experiments of random Hankel tensor completion and image restoration examples.展开更多
Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_...Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).展开更多
In the paper,a class of functions with bounded turnings involving cardioid domain,are studied in the region of the unit disc.The bounds of|a_(5)|,|a_(6)|,|a_(7)|and the fourth Hankel determinant are obtained,which are...In the paper,a class of functions with bounded turnings involving cardioid domain,are studied in the region of the unit disc.The bounds of|a_(5)|,|a_(6)|,|a_(7)|and the fourth Hankel determinant are obtained,which are more accurate than those obtained by Srivastava.展开更多
本文主要研究了Fock空间Fαp上小Hankel算子hφ的有界性和紧性,得到了hφ在Fαp上有界的充分必要条件是其符号φ属于Fock空间Fα2∞;hφ在Fαp上紧的充分必要条件是φ属于fα2∞。This paper mainly studies the boundedness and compac...本文主要研究了Fock空间Fαp上小Hankel算子hφ的有界性和紧性,得到了hφ在Fαp上有界的充分必要条件是其符号φ属于Fock空间Fα2∞;hφ在Fαp上紧的充分必要条件是φ属于fα2∞。This paper mainly studies the boundedness and compactness of the small Hankel operator hφon Fock space Fαp. It is found that the necessary and sufficient condition for hφbeing bounded on Fαpis that its symbol φbelongs to Fock space Fα2∞;the necessary and sufficient condition for hφbeing compact on Fαpis that φbelongs to fα2∞.展开更多
本文给出了Fock空间上两个Hankel算子乘积的有界性的必要条件描述,且结合反例证明此条件是两个Hankel算子乘积的有界性的必要不充分条件。In this paper, we give a description of the necessary condition for boundedness of the pro...本文给出了Fock空间上两个Hankel算子乘积的有界性的必要条件描述,且结合反例证明此条件是两个Hankel算子乘积的有界性的必要不充分条件。In this paper, we give a description of the necessary condition for boundedness of the product of two Hankel operators on Fock space, and prove that this condition is a necessary and insufficient condition for boundedness of the product of two Hankel operators.展开更多
Here we complete our work on the asymptotics of Hankel determinants studying the case wherein the entries are “ultrarapidly”-varying functions in the sense that their logarithms are rapidly varying. Moreover, the la...Here we complete our work on the asymptotics of Hankel determinants studying the case wherein the entries are “ultrarapidly”-varying functions in the sense that their logarithms are rapidly varying. Moreover, the last results in the paper highlight analogies between algebraic identities for Hankelians with special entries and asymptotic relations valid for large classes of entries.展开更多
文摘加速邻近梯度算法是求解张量补全问题的经典方法之一,但将该算法应用到Hankel结构张量补全时,无法保证补全的张量能够保持Hankel结构。因此,本文基于加速邻近梯度算法的框架,提出了一种保Hankel结构的加速邻近梯度算法。该算法在每次迭代中利用l∞-模投影算子生成Hankel结构张量。在理论上,本文证明了新算法在合理假设条件下的收敛性。最后,通过随机Hankel张量补全与图像修复实例的数值实验验证了新算法的有效性。The accelerated proximal gradient algorithm is one of the classic methods for solving tensor completion problems. However, when applied to Hankel structured tensor completion, it cannot guarantee that the completed tensor can maintain the Hankel structure. Therefore, based on the framework of the accelerated proximal gradient algorithm, this paper proposes a new accelerated proximal gradient algorithm that can preserve the Hankel structure. In each iteration of the algorithm, utilizing the l∞-norm projection and the fast singular value thresholding method ensures that the generated tensor preserves the Hankel structure. Moreover, this paper proves the convergence of the new algorithm under reasonable assumptions. Finally, the effectiveness of the new algorithm is verified through numerical experiments of random Hankel tensor completion and image restoration examples.
文摘Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).
基金Supported by the Natural Science Foundation of Anhui Provincial Department of Education(Grant Nos.KJ2020A 0993KJ2020ZD74)+2 种基金the High-Level Talent Research Start-Up Project(Grant No.DC2300000286)the Foundation of Guangzhou Civil Aviation College(Grant Nos.22X041824X4412).
文摘In the paper,a class of functions with bounded turnings involving cardioid domain,are studied in the region of the unit disc.The bounds of|a_(5)|,|a_(6)|,|a_(7)|and the fourth Hankel determinant are obtained,which are more accurate than those obtained by Srivastava.
文摘本文主要研究了Fock空间Fαp上小Hankel算子hφ的有界性和紧性,得到了hφ在Fαp上有界的充分必要条件是其符号φ属于Fock空间Fα2∞;hφ在Fαp上紧的充分必要条件是φ属于fα2∞。This paper mainly studies the boundedness and compactness of the small Hankel operator hφon Fock space Fαp. It is found that the necessary and sufficient condition for hφbeing bounded on Fαpis that its symbol φbelongs to Fock space Fα2∞;the necessary and sufficient condition for hφbeing compact on Fαpis that φbelongs to fα2∞.
文摘本文给出了Fock空间上两个Hankel算子乘积的有界性的必要条件描述,且结合反例证明此条件是两个Hankel算子乘积的有界性的必要不充分条件。In this paper, we give a description of the necessary condition for boundedness of the product of two Hankel operators on Fock space, and prove that this condition is a necessary and insufficient condition for boundedness of the product of two Hankel operators.
文摘Here we complete our work on the asymptotics of Hankel determinants studying the case wherein the entries are “ultrarapidly”-varying functions in the sense that their logarithms are rapidly varying. Moreover, the last results in the paper highlight analogies between algebraic identities for Hankelians with special entries and asymptotic relations valid for large classes of entries.
