Article
Mathematics, Applied
Li He
Summary: This paper examines the properties of the Hardy-Sobolev space H82 and its relation to the Dirichlet space. By proving the equivalence between the density of the range of Cw in H82 and the density of polynomials in a specific Dirichlet space, several conclusions are drawn.
Article
Mathematics, Applied
Aastha Malhotra, Anuradha Gupta
Summary: The article investigates the complex symmetric structure of the generalized weighted composition operator on the Fock space, and provides characterizations for the operator to be Hermitian on this space.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Xin Guo, Maofa Wang
Summary: This paper completely characterizes the boundedness of difference of weighted composition operators between weak and strong vector-valued Bergman spaces in three terms: one is a function theoretic characterization of Julia-Caratheodory type, the second is a power type characterization and the other is a measure theoretic characterization of Carleson type. Furthermore, the paper investigates the bounded difference of composition operators for corresponding vector-valued Fock space case, which contrasts with some phenomenon in the setting of vector-valued Bergman space.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Kaikai Han, Maofa Wang
Summary: This paper studies weighted composition operators on F-2 and proves that these operators are complex symmetric. In contrast, the analysis on H-2(D) is also discussed, along with the characterization of Hermitian weighted composition operators and algebraic weighted composition operators. Additionally, the cyclicity of complex symmetric weighted composition operators and their preservation of frames on F-2 are investigated.
SCIENCE CHINA-MATHEMATICS
(2022)
Article
Mathematics
Xin Guo, Maofa Wang
Summary: This paper presents a compactness criterion for composition operators on the weighted Bergman space, showing the equivalence of compactness on different spaces.
POTENTIAL ANALYSIS
(2022)
Article
Mathematics
Guangfu Cao, Li He, Ji Li, Minxing Shen
Summary: This paper provides a boundedness criterion for the integral operator S-phi on the fractional Fock-Sobolev space. The criterion extends previous research and utilizes multipliers on the fractional Hermite-Sobolev space as the main approach.
MATHEMATISCHE ZEITSCHRIFT
(2022)
Article
Mathematics, Applied
Miguel Lacruz, Fernando Leon-Saavedra, Srdjan Petrovic, Luis Rodriguez-Piazza
Summary: This paper discusses the problem of extended eigenvalues for bounded linear operators on complex Hilbert spaces, with a particular focus on the composition operators induced on the Hardy space by linear fractional transformations on the unit disk. The results presented in the paper offer a comprehensive solution to this problem.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Tom Carroll, Clifford Gilmore
Summary: Bounded weighted composition operators and compact weighted composition operators on Fock spaces have been characterized with a refined description in terms of multiplier order and type, including a complete description of zero-free multipliers and explicit asymptotics for operator iterates. It has been shown that weighted composition operators on the Fock space cannot be supercyclic.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics
Zhiyuan Xu, Zicong Yang, Zehua Zhou
Summary: This paper solves a new problem regarding complex symmetry by characterizing linear combinations of composition operators on the Fock space. The normality and self-adjointness of complex symmetric linear combinations of composition operators are considered simultaneously.
ARCHIV DER MATHEMATIK
(2022)
Article
Mathematics, Applied
Jianhui Hu, Songxiao Li, Dan Qu
Summary: This paper provides complete characterizations of positive Borel measures that lead to bounded or compact differentiation operators in Fock spaces. It also discusses the boundedness and compactness of generalized weighted composition operators in Fock spaces, as well as studies the essential norm of these operators.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2021)
Article
Mathematics, Applied
Manish Kumar, Tusharakanta Pradhan
Summary: The paper focuses on defining and studying a class of pseudo-differential operators (PDOs) associated with the symbol b(x, y) and linear canonical transform (LCT), as well as their applications in solving boundary value problems of generalized partial differential equations. Boundedness properties and new integral operators are investigated to better understand the composition of these operators and their applications in obtaining closed form solutions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics
Pham Viet Hai
Summary: The study focuses on unbounded linear operators created from a finite number of composition operators on Fock space, characterizing the real and complex symmetries of these operators.
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics
Mahmood Haji Shaabani, Mahsa Fatehi, Christopher N. B. Hammond
Summary: In this study, we examine the numerical range of a bounded weighted composition operator C-psi, C-phi on the Fock space F-2, providing necessary and sufficient conditions for the interior of the numerical range, as well as characterizing the presence of corner points. Additionally, we determine the numerical range of various weighted composition operators, including cases where the numerical range does not contain 0.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
(2022)
Article
Mathematics
Pham Thi Lieu, Dinh Thi Thu, Pham Trong Tien
Summary: The study primarily focuses on the boundedness and compactness of linear combinations of two composition operators acting between different Fock spaces in several variables.
VIETNAM JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics
Yiyuan Zhang, Guangfu Cao, Li He
Summary: This paper investigates the boundedness of Toeplitz and Hankel products on Fock-Sobolev space, and characterizes the boundedness of Toeplitz and Hankel operators with elements from P.
CHINESE ANNALS OF MATHEMATICS SERIES B
(2022)
