Similarity to the backward shift operator on the Dirichlet space

2016 ◽  
Vol 76 (1) ◽  
pp. 133-140 ◽  
Author(s):  
Hyun-Kyoung Kwon
Keyword(s):  
Shift Operator ◽  
Dirichlet Space ◽  
Backward Shift

scholarly journals Li-Yorke chaotic eigen set of the backward shift operator on ℓ2(𝕅)

2020 ◽  
Vol 7 (1) ◽  
pp. 180-182
Author(s):  
B. Sanooj ◽  
P.B. Vinodkumar
Keyword(s):  
Positive Integer ◽  
Complex Plane ◽  
Shift Operator ◽  
Integer Multiple ◽  
Backward Shift

AbstractIn this paper, we prove our main result that the Li-Yorke chaotic eigen set of a positive integer multiple of the backward shift operator on ℓ2 (𝕅) is a disk in the complex plane 𝔺 and the union of such Li-Yorke chaotic eigen set’s is the whole complex plane 𝔺.

State dependent versions of the space-time fractional poisson process

2020 ◽  
Vol 23 (5) ◽  
pp. 1483-1505
Author(s):  
Kuldeep Kumar Kataria ◽  
Palaniappan Vellaisamy
Keyword(s):  
Poisson Process ◽  
Shift Operator ◽  
Adomian Decomposition Method ◽  
Space Time ◽  
Counting Processes ◽  
State Dependency ◽  
Fractional Poisson Process ◽  
State Dependent ◽  
Adomian Decomposition ◽  
Backward Shift

Abstract In this paper, we introduce and study two counting processes by considering state dependency on the order of fractional derivative as well as on the exponent of backward shift operator involved in the governing difference-differential equations of the state probabilities of space-time fractional Poisson process. The Adomian decomposition method is employed to obtain their state probabilities and then their Laplace transforms are evaluated. Also, the compound versions of these state dependent models are studied and the corresponding governing fractional integral equations of their state probabilities are obtained.

scholarly journals Universal approximation theorem for Dirichlet series

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
O. Demanze ◽  
A. Mouze
Keyword(s):  
Dirichlet Series ◽  
Simultaneous Approximation ◽  
Shift Operator ◽  
Approximation Theorem ◽  
Extension Theorem ◽  
Universal Approximation ◽  
Derivation Operator ◽  
Backward Shift ◽  
The Right ◽  
Density Results

The paper deals with an extension theorem by Costakis and Vlachou on simultaneous approximation for holomorphic function to the setting of Dirichlet series, which are absolutely convergent in the right half of the complex plane. The derivation operator used in the analytic case is substituted by a weighted backward shift operator in the Dirichlet case. We show the similarities and extensions in comparing both results. Several density results are proved that finally lead to the main theorem on simultaneous approximation.

TOPOLOGICAL CHAOS FOR A CLASS OF LINEAR MODELS

1992 ◽  
Vol 02 (01) ◽  
pp. 79-90 ◽  
Author(s):  
V. PROTOPOPESCU ◽  
Y.Y. AZMY
Keyword(s):  
Banach Space ◽  
Linear Models ◽  
Shift Operator ◽  
Topological Transitivity ◽  
Linear Rate ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Topological Chaos ◽  
Backward Shift ◽  
The Relationship

We construct an example of linear rate equation in the Banach space of summable sequences, l1, that exhibits the three properties required as signature of topological chaos, namely: (i) topological transitivity, (ii) dense periodic orbits, and (iii) positive Lyapunov exponents. The example is based on the properties of the backward shift operator on the Banach space l1. Since linear chaos in the sense described above can occur only in an infinite-dimensional setting, possible finite-dimensional approximate manifestations are investigated. The relationship between the linear backward shift and the nonlinear Bernoulli shift is also discussed.

scholarly journals Cyclic vectors and invariant subspaces for the backward shift operator

1970 ◽  
Vol 20 (1) ◽  
pp. 37-76 ◽  
Author(s):  
R. G. Douglas ◽  
H. S. Shapiro ◽  
A. L. Shields
Keyword(s):  
Shift Operator ◽  
Invariant Subspaces ◽  
Cyclic Vectors ◽  
Backward Shift
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