scholarly journals Self-adjoint truncated Toeplitz operators on finite-dimensional model spaces

2012 ◽  
Vol 23 (3) ◽  
pp. 388-400
Author(s):  
Donald Sarason
Keyword(s):  
Toeplitz Operators ◽  
Dimensional Model ◽  
Finite Dimensional ◽  
Model Spaces

scholarly journals Asymmetric Truncated Hankel Operators: Rank One, Matrix Representation

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Firdaws Rahmani ◽  
Yufeng Lu ◽  
Ran Li
Keyword(s):  
Toeplitz Operators ◽  
Matrix Representation ◽  
Hankel Operators ◽  
Natural Generalization ◽  
Dimensional Model ◽  
Finite Dimensional ◽  
Rank One ◽  
Model Spaces ◽  
The One ◽  
Interpolating Blaschke Products

Asymmetric truncated Hankel operators are the natural generalization of truncated Hankel operators. In this paper, we determine all rank one operators of this class. We explore these operators on finite-dimensional model spaces, in particular, their matrix representation. We also give their matrix representation and the one for asymmetric truncated Toeplitz operators in the case of model spaces associated to interpolating Blaschke products.

scholarly journals Matrix Representations of Asymmetric Truncated Toeplitz Operators

2020 ◽  
Author(s):  
Joanna Jurasik ◽  
Bartosz Łanucha
Keyword(s):  
Toeplitz Operators ◽  
Dimensional Model ◽  
Matrix Representations ◽  
Finite Dimensional ◽  
The Matrix ◽  
Model Spaces

Abstract In this paper, we describe the matrix representations of asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces $$K_1$$ K 1 and $$K_2$$ K 2 . The novelty of our approach is that here we consider matrix representations computed with respect to bases of different type in $$K_1$$ K 1 and $$K_2$$ K 2 (for example, kernel basis in $$K_1$$ K 1 and conjugate kernel basis in $$K_2$$ K 2 ). We thus obtain new matrix characterizations which are simpler than the ones already known for asymmetric truncated Toeplitz operators.

Finite-Dimensional Model Spaces

2018 ◽  
pp. 261-290
Author(s):  
Stephan Ramon Garcia ◽  
Javad Mashreghi ◽  
William T. Ross
Keyword(s):  
Dimensional Model ◽  
Finite Dimensional ◽  
Model Spaces

scholarly journals Complete Bredon cohomology and its applications to hierarchically defined groups

2016 ◽  
Vol 161 (1) ◽  
pp. 143-156
Author(s):  
BRITA E. A. NUCINKIS ◽  
NANSEN PETROSYAN
Keyword(s):  
Integral Characteristic ◽  
Linear Groups ◽  
Dimensional Model ◽  
Classifying Space ◽  
Soluble Groups ◽  
3 Dimensional ◽  
Cyclic Groups ◽  
Bredon Cohomology ◽  
Finite Dimensional ◽  
The Family

AbstractBy considering the Bredon analogue of complete cohomology of a group, we show that every group in the class$\cll\clh^{\mathfrak F}{\mathfrak F}$of type Bredon-FP∞admits a finite dimensional model for$E_{\frak F}G$.We also show that abelian-by-infinite cyclic groups admit a 3-dimensional model for the classifying space for the family of virtually nilpotent subgroups. This allows us to prove that for$\mathfrak {F}$, the class of virtually cyclic groups, the class of$\cll\clh^{\mathfrak F}{\mathfrak F}$-groups contains all locally virtually soluble groups and all linear groups over${\mathbb{C}}$of integral characteristic.

Draft: Stick-Slip Motions of a Rotor-Stator System

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Nicholas Vlajic ◽  
Chien-Min Liao ◽  
Hamad Karki ◽  
Balakumar Balachandran
Keyword(s):  
Dry Friction ◽  
Torsional Oscillation ◽  
Flexible Structures ◽  
Oil Well ◽  
Torsional Vibrations ◽  
Dimensional Model ◽  
Torsional Mode ◽  
Stick Slip ◽  
Finite Dimensional ◽  
Motion State

In the current study, the authors examine the torsional vibrations of a rotor enclosed within a stator subjected to dry friction. Through the experiments, it is demonstrated that forward whirling of the rotor occurs while in contact with the stator, backward whirling occurs with contact, as well as impacting motions, which are characterized by nonsynchronous whirling with rotor-stator collisions. While undergoing these motions, the torsional oscillations are excited by stick-slip interactions. Experimental data are presented to show the presence of a stable torsional mode dominated motion while subjected to stick-slip forces during dry-friction whirling. In this motion state, the torsional oscillation response occurs at a combination of frequencies including drive and whirl frequencies. A finite dimensional model is constructed and simulations carried out by using this model are able to capture the system dynamics, including the torsional responses observed during dry-friction whirling. Numerical results obtained by using this model are consistent with experimental observations. The findings of this study are relevant to whirling motions experienced by rotating, long flexible structures, such as drill strings used in oil-well explorations.

Unconstrained and Constrained Mode Expansions for a Flexible Slewing Link

1988 ◽  
Vol 110 (4) ◽  
pp. 416-421 ◽  
Author(s):  
Enrique Barbieri ◽  
U¨mit O¨zgu¨ner
Keyword(s):  
Equations Of Motion ◽  
Linear Equations ◽  
Quantitative Comparison ◽  
Mode Shapes ◽  
Dimensional Model ◽  
Finite Dimensional ◽  
Linear Equations Of Motion ◽  
Aluminum Beam

The linear equations of motion of a uniform flexible slewing link which were derived via Hamilton’s Extended Principle are considered. These equations account for the coupling between bending and rigid modes. Unconstrained and constrained mode expansions are investigated and a quantitative comparison is made between the frequency equations and associated mode shapes. A finite dimensional model is derived using the assumed modes method and the theoretical frequencies are verified with an experimental counterbalanced aluminum beam.

Periodic cohomology and subgroups with bounded Bredon cohomological dimension

2008 ◽  
Vol 144 (2) ◽  
pp. 329-336 ◽  
Author(s):  
JANG HYUN JO ◽  
BRITA E. A. NUCINKIS
Keyword(s):  
Free Group ◽  
Amenable Group ◽  
Cohomological Dimension ◽  
Dimensional Model ◽  
Torsion Free Group ◽  
Bredon Cohomology ◽  
Finite Dimensional ◽  
Torsion Free

AbstractMislin and Talelli showed that a torsion-free group in$\HF$with periodic cohomology after some steps has finite cohomological dimension. In this note we look at similar questions for groups with torsion by considering Bredon cohomology. In particular we show that every elementary amenable group acting freely and properly on some$\R^n$×Smadmits a finite dimensional model for$\E$G.

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