Reducing subspaces: Definitions, properties and algorithms

1983 ◽  
pp. 58-73 ◽  
Author(s):  
Paul Van Dooren
Keyword(s):  
Reducing Subspaces

scholarly journals Reducing subspaces of weighted shift operators

2002 ◽  
Vol 130 (9) ◽  
pp. 2631-2639 ◽  
Author(s):  
Michael Stessin ◽  
Kehe Zhu
Keyword(s):  
Weighted Shift ◽  
Shift Operators ◽  
Reducing Subspaces

Reducing subspaces for the product of a forward and a backward operator-weighted shifts

2021 ◽  
Vol 501 (2) ◽  
pp. 125206
Author(s):  
Xu Tang ◽  
Caixing Gu ◽  
Yufeng Lu ◽  
Yanyue Shi
Keyword(s):  
Weighted Shifts ◽  
Reducing Subspaces

Joint dilation scaling sets on the reducing subspaces

2012 ◽  
Vol 3 (3) ◽  
Author(s):  
Niraj K. Shukla ◽  
Rajeshwari Dubey
Keyword(s):  
Reducing Subspaces

scholarly journals TIME-SHIFTS GENERALIZED MULTIRESOLUTION ANALYSIS OVER DYADIC-SCALING REDUCING SUBSPACES

2004 ◽  
Vol 02 (03) ◽  
pp. 237-248 ◽  
Author(s):  
NHAN LEVAN ◽  
CARLOS S. KUBRUSLY
Keyword(s):  
Function Space ◽  
Multiresolution Analysis ◽  
Time Shift ◽  
Orthonormal Wavelet ◽  
Reducing Subspaces ◽  
Wandering Subspace ◽  
Generalized Multiresolution Analysis

A Generalized Multiresolution Analysis (GMRA) associated with a wavelet is a sequence of nested subspaces of the function space ℒ2(ℝ), with specific properties, and arranged in such a way that each of the subspaces corresponds to a scale 2m over all time-shifts n. These subspaces can be expressed in terms of a generating-wandering subspace — of the dyadic-scaling operator — spanned by orthonormal wavelet-functions — generated from the wavelet. In this paper we show that a GMRA can also be expressed in terms of subspaces for each time-shift n over all scales 2m. This is achieved by means of "elementary" reducing subspaces of the dyadic-scaling operator. Consequently, Time-Shifts GMRA associated with wavelets, as well as "sub-GMRA" associated with "sub-wavelets" will then be introduced.

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

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.

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