The backward shift on 𝐻²

2006 ◽  
pp. 179-200 ◽  
Author(s):  
Joseph Cima ◽  
Alec Matheson ◽  
William Ross
Keyword(s):  
Backward Shift

The range of block Hankel operators

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3237-3243
Author(s):  
In Hwang ◽  
In Kim ◽  
Sumin Kim
Keyword(s):  
Hardy Space ◽  
Invariant Subspace ◽  
Hankel Operators ◽  
Coprime Factorization ◽  
Backward Shift ◽  
Vector Valued

In this note we give a connection between the closure of the range of block Hankel operators acting on the vector-valued Hardy space H2Cn and the left coprime factorization of its symbol. Given a subset F ? H2Cn, we also consider the smallest invariant subspace S*F of the backward shift S* that contains F.

Weighted backward shift operators with invariant distributionally scrambled subsets

2017 ◽  
Vol 8 (2) ◽  
pp. 199-210 ◽  
Author(s):  
Xinxing Wu ◽  
Lidong Wang ◽  
Guanrong Chen
Keyword(s):  
Shift Operators ◽  
Backward Shift

scholarly journals The role of action intentionality and effector in the subjective expansion of temporal duration after saccadic eye movements

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
David Melcher ◽  
Devpriya Kumar ◽  
Narayanan Srinivasan
Keyword(s):  
Eye Movements ◽  
Visual Processing ◽  
Saccadic Eye Movements ◽  
Intentional Binding ◽  
Opposite Pattern ◽  
Motor Action ◽  
Saccade Onset ◽  
Backward Shift ◽  
The Moment

Abstract Visual perception is based on periods of stable fixation separated by saccadic eye movements. Although naive perception seems stable (in space) and continuous (in time), laboratory studies have demonstrated that events presented around the time of saccades are misperceived spatially and temporally. Saccadic chronostasis, the “stopped clock illusion”, represents one such temporal distortion in which the movement of the clock hand after the saccade is perceived as lasting longer than usual. Multiple explanations for chronostasis have been proposed including action-backdating, temporal binding of the action towards the moment of its effect (“intentional binding”) and post-saccadic temporal dilation. The current study aimed to resolve this debate by using different types of action (keypress vs saccade) and varying the intentionality of the action. We measured both perceived onset of the motor action and perceived onset of an auditory tone presented at different delays after the keypress/saccade. The results showed intentional binding for the keypress action, with perceived motor onset shifted forwards in time and the time of the tone shifted backwards. Saccades resulted in the opposite pattern, showing temporal expansion rather than compression, especially with cued saccades. The temporal illusion was modulated by intentionality of the movement. Our findings suggest that saccadic chronostasis is not solely dependent on a backward shift in perceived saccade onset, but instead reflects a temporal dilation. This percept of an effectively “longer” period at the beginning of a new fixation may reflect the pattern of suppressed, and then enhanced, visual processing around the time of saccades.

scholarly journals Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd2π-Periodic Functions

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Tamás Kalmár-Nagy ◽  
Márton Kiss
Keyword(s):  
Nonlinear Systems ◽  
Linear Operator ◽  
Linear Systems ◽  
Chaotic Dynamics ◽  
Periodic Points ◽  
Complex Behavior ◽  
Periodic Functions ◽  
Infinite Dimensional ◽  
Backward Shift ◽  
Principal Value

Not just nonlinear systems but infinite-dimensional linear systems can exhibit complex behavior. It has long been known that twice the backward shift on the space of square-summable sequencesl2displays chaotic dynamics. Here we construct the corresponding operatorCon the space of2π-periodic odd functions and provide its representation involving a Principal Value Integral. We explicitly calculate the eigenfunction of this operator, as well as its periodic points. We also provide examples of chaotic and unbounded trajectories ofC.

scholarly journals Pseudocontinuations and the backward shift

1998 ◽  
Vol 47 (1) ◽  
pp. 0-0 ◽  
Author(s):  
Alexandru Aleman ◽  
Stefan Richter ◽  
William T. Ross
Keyword(s):  
Backward Shift
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