scholarly journals Common reducing subspace model and network alternation analysis

Biometrics ◽  
2019 ◽  
Vol 75 (4) ◽  
pp. 1109-1120 ◽  
Author(s):  
Wenjing Wang ◽  
Xin Zhang ◽  
Lexin Li
Keyword(s):  
Reducing Subspace

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 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 SPECTRUM, NUMERICAL RANGE AND DAVIS-WIELANDT SHELL OF A NORMAL OPERATOR

2009 ◽  
Vol 51 (1) ◽  
pp. 91-100 ◽  
Author(s):  
CHI-KWONG LI ◽  
YIU-TUNG POON
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Convex Set ◽  
Numerical Range ◽  
Normal Operator ◽  
Additional Information ◽  
Commuting Operators ◽  
Boundary Points ◽  
Reducing Subspace ◽  
Joint Numerical Range

AbstractWe denote the numerical range of the normal operator T by W(T). A characterization is given to the points in W(T) that lie on the boundary. The collection of such boundary points together with the interior of the the convex hull of the spectrum of T will then be the set W(T). Moreover, it is shown that such boundary points reveal a lot of information about the normal operator. For instance, such a boundary point always associates with an invariant (reducing) subspace of the normal operator. It follows that a normal operator acting on a separable Hilbert space cannot have a closed strictly convex set as its numerical range. Similar results are obtained for the Davis-Wielandt shell of a normal operator. One can deduce additional information of the normal operator by studying the boundary of its Davis-Wielandt shell. Further extension of the result to the joint numerical range of commuting operators is discussed.

Spectral Inclusion and C.N.E.

1982 ◽  
Vol 34 (4) ◽  
pp. 883-887 ◽  
Author(s):  
A. R. Lubin
Keyword(s):  
Hilbert Space ◽  
Linear Operators ◽  
Normal Extension ◽  
Unitary Equivalence ◽  
Bounded Linear ◽  
Multi Index ◽  
Reducing Subspace ◽  
Normal Operators ◽  
Image Position ◽  
Minimal Normal Extension

1. An n-tuple S = (S1, …, Sn) of commuting bounded linear operators on a Hilbert space H is said to have commuting normal extension if and only if there exists an n-tuple N = (N1, …, Nn) of commuting normal operators on some larger Hilbert space K ⊃ H with the restrictions Ni|H = Si, i = 1, …, n. If we takethe minimal reducing subspace of N containing H, then N is unique up to unitary equivalence and is called the c.n.e. of S. (Here J denotes the multi-index (j1, …, jn) of nonnegative integers and N*J = N1*jl … Nn*jn and we emphasize that c.n.e. denotes minimal commuting normal extension.) If n = 1, then S1 = S is called subnormal and N1 = N its minimal normal extension (m.n.e.).

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].

scholarly journals Supporting multi-point fan design with dimension reduction

2020 ◽  
Vol 124 (1279) ◽  
pp. 1371-1398 ◽  
Author(s):  
P. Seshadri ◽  
S. Yuchi ◽  
G.T. Parks ◽  
S. Shahpar
Keyword(s):  
Dimension Reduction ◽  
Variance Estimation ◽  
Numerical Study ◽  
Computational Cost ◽  
Inverse Regression ◽  
Variable Projection ◽  
Reducing Subspace ◽  
Reducing Subspaces ◽  
Reduction Methods ◽  
Dimension Reducing

AbstractMotivated by the idea of turbomachinery active subspace performance maps, this paper studies dimension reduction in turbomachinery 3D CFD simulations. First, we show that these subspaces exist across different blades—under the same parametrisation—largely independent of their Mach number or Reynolds number. This is demonstrated via a numerical study on three different blades. Then, in an attempt to reduce the computational cost of identifying a suitable dimension reducing subspace, we examine statistical sufficient dimension reduction methods, including sliced inverse regression, sliced average variance estimation, principal Hessian directions and contour regression. Unsatisfied by these results, we evaluate a new idea based on polynomial variable projection—a non-linear least-squares problem. Our results using polynomial variable projection clearly demonstrate that one can accurately identify dimension reducing subspaces for turbomachinery functionals at a fraction of the cost associated with prior methods. We apply these subspaces to the problem of comparing design configurations across different flight points on a working line of a fan blade. We demonstrate how designs that offer a healthy compromise between performance at cruise and sea-level conditions can be easily found by visually inspecting their subspaces.

On wavelet induced isomorphisms for reducing subspaces

2016 ◽  
Vol 14 (03) ◽  
pp. 1650009 ◽  
Author(s):  
Swati Srivastava ◽  
G. C. S. Yadav
Keyword(s):  
Hardy Space ◽  
Wavelet Sets ◽  
Reducing Subspace ◽  
Wavelet Set ◽  
Michigan Math ◽  
Reducing Subspaces ◽  
Real Anal ◽  
New Construction ◽  
Classical Hardy Space

In this paper, we adapt the notion of a wavelet induced isomorphism of [Formula: see text] associated with a wavelet set, introduced in [E. J. Ionascu, A new construction of wavelet sets, Real Anal. Exchange 28(2) (2002/03) 593–610], to the case of an [Formula: see text]-wavelet set, where [Formula: see text] is a reducing subspace [X. Dai and S. Lu, Wavelets in subspaces, Michigan Math. J. 43 (1996) 81–98]. We characterize all these wavelet induced isomorphisms similar to those given in Ionascu paper and provide specific examples of this theory in the case of symmetric [Formula: see text]-wavelet sets. Examples when [Formula: see text] is the classical Hardy space are also considered.

Sign in / Sign up

Export Citation Format

Share Document