scholarly journals Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Yanyue Shi ◽  
Na Zhou
Keyword(s):  
Bergman Space ◽  
Multiplication Operators ◽  
Direct Sum ◽  
Reducing Subspace ◽  
Reducing Subspaces

We consider the reducing subspaces ofMzNonAα2(Dk), wherek≥3,zN=z1N1⋯zkNk, andNi≠Njfori≠j. We prove that each reducing subspace ofMzNis a direct sum of some minimal reducing subspaces. We also characterize the minimal reducing subspaces in the cases thatα=0andα∈(-1,+∞)∖Q, respectively. Finally, we give a complete description of minimal reducing subspaces ofMzNonAα2(D3)withα>-1.

scholarly journals Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces

2017 ◽  
Vol 4 (1) ◽  
pp. 84-119 ◽  
Author(s):  
Caixing Gu ◽  
Shuaibing Luo ◽  
Jie Xiao
Keyword(s):  
Bergman Space ◽  
Blaschke Product ◽  
Riemann Surfaces ◽  
Dirichlet Space ◽  
Multiplication Operator ◽  
Multiplication Operators ◽  
Finite Blaschke Product ◽  
Full Characterization ◽  
Reducing Subspaces

AbstractThis paper gives a full characterization of the reducing subspaces for the multiplication operator Mϕ on the Dirichlet space with symbol of finite Blaschke product ϕ of order 5I 6I 7. The reducing subspaces of Mϕ on the Dirichlet space and Bergman space are related. Our strategy is to use local inverses and Riemann surfaces to study the reducing subspaces of Mϕ on the Bergman space. By this means, we determine the reducing subspaces of Mϕ on the Dirichlet space and answer some questions of Douglas-Putinar-Wang in [6].

scholarly journals Classification of Reducing Subspaces of a Class of Multiplication Operators on the Bergman Space via the Hardy Space of the Bidisk

2010 ◽  
Vol 62 (2) ◽  
pp. 415-438 ◽  
Author(s):  
Shunhua Sun ◽  
Dechao Zheng ◽  
Changyong Zhong
Keyword(s):  
Hardy Space ◽  
Unit Disk ◽  
Bergman Space ◽  
Blaschke Product ◽  
Multiplication Operator ◽  
Multiplication Operators ◽  
Reducing Subspaces

AbstractIn this paper we obtain a complete description of nontrivial minimal reducing subspaces of the multiplication operator by a Blaschke product with four zeros on the Bergman space of the unit disk via the Hardy space of the bidisk.

Reducing Subspace of Analytic Toeplitz Operators on the Bergman Space

2004 ◽  
Vol 49 (3) ◽  
pp. 387-395 ◽  
Author(s):  
Junyun Hu ◽  
Shunhua Sun ◽  
Xianmin Xu ◽  
Dahai Yu
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Reducing Subspace

scholarly journals Reducing subspaces for analytic multipliers of the Bergman space

2012 ◽  
Vol 263 (6) ◽  
pp. 1744-1765 ◽  
Author(s):  
Ronald G. Douglas ◽  
Mihai Putinar ◽  
Kai Wang
Keyword(s):  
Bergman Space ◽  
Reducing Subspaces

Semi-Orthogonal Parseval Wavelets Frames on Local Fields and Applications in Manufacturing Science

2013 ◽  
Vol 712-715 ◽  
pp. 2464-2468
Author(s):  
Shi Heng Wang
Keyword(s):  
Local Fields ◽  
Affine Subspace ◽  
Parseval Frame ◽  
Direct Sum ◽  
Reducing Subspaces ◽  
Dilation Factor ◽  
Definition Of ◽  
Frame Wavelets ◽  
Manufacturing Science ◽  
Orthogonal Frame

Manufacturing science focuses on understanding problems from the perspective of the stakeholders involved and then applying manufacturing science as needed. We investigate semi-orthogonal frame wavelets and Parseval frame wavelets in with a dilation factor. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces. This result is obtained through considering the basicquestion as to when the orthogonal complement of an afffine subspace in another one is still affine subspace.The definition of multiple pseudofames for subspaces with integer translation is proposed. The notion of a generalized multiresolution structure of is also introduced. The construction of a generalized multireso-lution structure of Paley-Wiener subspaces of is investigated.

Weak nonhomogeneous wavelet dual frames for Walsh reducing subspace of L2(ℝ+)

2021 ◽  
pp. 2150040
Author(s):  
Yan Zhang ◽  
Yun-Zhang Li
Keyword(s):  
Extension Principle ◽  
Transform Domain ◽  
Wavelet Frames ◽  
Dual Frames ◽  
Reducing Subspace ◽  
Reducing Subspaces ◽  
Extension Principles ◽  
Dual Wavelet Frames ◽  
Dual Wavelet ◽  
Fourier Transform Domain

In wavelet analysis, refinable functions are the bases of extension principles for constructing (weak) dual wavelet frames for [Formula: see text] and its reducing subspaces. This paper addresses refinable function-based dual wavelet frames construction in Walsh reducing subspaces of [Formula: see text]. We obtain a Walsh–Fourier transform domain characterization for weak [Formula: see text]-adic nonhomogeneous dual wavelet frames; and present a mixed oblique extension principle for constructing weak [Formula: see text]-adic nonhomogeneous dual wavelet frames in Walsh reducing subspaces of [Formula: see text].

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