scholarly journals On unilateral shift operators and C0-operators

1992 ◽  
Vol 53 (1) ◽  
pp. 137-142
Author(s):  
Il Bong Jung ◽  
Yong Chan Kim
Keyword(s):  
Hilbert Space ◽  
Shift Operator ◽  
Matrix Form ◽  
Operator Matrix ◽  
Unilateral Shift ◽  
Shift Operators

AbstractLet S(n) be a unilateral shift operator on a Hilbert space of multiplicity n. In this paper, we prove a generalization of the theorem that if S(1) is unitarily equivalent to an operator matrix form relative to a decomposition ℳ ⊕ N, then E is in a certain class C0 which will be defined below.

scholarly journals SUSUSY Quantum Mechanics

1997 ◽  
Vol 12 (01) ◽  
pp. 171-176 ◽  
Author(s):  
David J. Fernández C.
Keyword(s):  
Quantum Mechanics ◽  
Shift Operator ◽  
Second Order ◽  
Parametric Family ◽  
First Order ◽  
Shift Operators ◽  
Exactly Solvable ◽  
Exactly Solvable Hamiltonians

The exactly solvable eigenproblems in Schrödinger quantum mechanics typically involve the differential "shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to be of first order. In this work, I discuss a technique to generate exactly solvable eigenproblems by using second order shift operators. The links between this method and SUSY are analysed. As an example, we show the existence of a two-parametric family of exactly solvable Hamiltonians, which contains the Abraham–Moses potentials as a particular case.

CHAOS IN A CLASS OF NONCONSTANT WEIGHTED SHIFT OPERATORS

2013 ◽  
Vol 23 (01) ◽  
pp. 1350010 ◽  
Author(s):  
XINXING WU ◽  
PEIYONG ZHU
Keyword(s):  
Positive Integer ◽  
Linear Space ◽  
Normed Linear Space ◽  
Shift Operator ◽  
Weighted Shift ◽  
Constructive Proof ◽  
Sufficient Condition ◽  
Weighted Shift Operator ◽  
Shift Operators ◽  
Devaney Chaos

In this paper, chaos generated by a class of nonconstant weighted shift operators is studied. First, we prove that for the weighted shift operator Bμ : Σ(X) → Σ(X) defined by Bμ(x0, x1, …) = (μ(0)x1, μ(1)x2, …), where X is a normed linear space (not necessarily complete), weak mix, transitivity (hypercyclity) and Devaney chaos are all equivalent to separability of X and this property is preserved under iterations. Then we get that [Formula: see text] is distributionally chaotic and Li–Yorke sensitive for each positive integer N. Meanwhile, a sufficient condition ensuring that a point is k-scrambled for all integers k > 0 is obtained. By using these results, a simple example is given to show that Corollary 3.3 in [Fu & You, 2009] does not hold. Besides, it is proved that the constructive proof of Theorem 4.3 in [Fu & You, 2009] is not correct.

Involutory *-antiautomorphisms in Toeplitz algebras

1988 ◽  
Vol 103 (3) ◽  
pp. 473-480
Author(s):  
P. J. Stacey
Keyword(s):  
Hilbert Space ◽  
Orthonormal Basis ◽  
Compact Operators ◽  
Complex Hilbert Space ◽  
Unilateral Shift ◽  
Integral Power

Let H be a separable complex Hilbert space with orthonormal basis {ei: i ∈ ℕ}, let s be the unilateral shift defined by sei = ei+1 for each i and let K be the algebra of compact operators on H. The present paper classifies the involutory *-anti-automorphisms in the C*-algebra C*(sn, K) generated by K and a positive integral power sn of s. It is shown that, up to conjugacy by *-automorphisms, there are two such involutory *-antiautomorphisms when n is even and one when n is odd.

Reply by author to discussion by Michael Schoenberger.

Geophysics ◽  
1968 ◽  
Vol 33 (4) ◽  
pp. 680-680
Author(s):  
John P. Burg
Keyword(s):  
Time Domain ◽  
Convolution Operator ◽  
Shift Operator ◽  
Time Shift ◽  
Weighted Sum ◽  
Sample Point ◽  
Shift Operators ◽  
Point Operator

The principal assertion of Schoenberger’s discussion appears to be that (3), which is correctly derived from equations in Section IV and corresponds to a space shift, should instead be written as (4), corresponding to a space sample. However, the space‐convolution operator corresponding to a seismometer is indeed meant to be a space‐shift operator. An array of seismometers is used as a weighted sum of space‐shift operators, just as a time‐domain, sample‐point operator is made up of a weighted sum of time‐shift operators. Equation (5.2), which Schoenberger indicates as being related to his (4), actually comes from (3) with x and y set to zero.

scholarly journals Some advances on essential spectra of one sided operator matrix with application

2021 ◽  
Author(s):  
Marwa Belghith ◽  
Nedra Moalla ◽  
Ines Walha
Keyword(s):  
Differential Equations ◽  
Unbounded Operator ◽  
Matrix Form ◽  
Operator Matrix ◽  
Essential Spectra ◽  
The One

This paper deals with a new description of the one sided operator matrix form, as a generalization of the case of the unbounded operator matrix with the non diagonal domain, to investigate some advances in the analysis of some essential spectra under weaker hypotheses then the one provided in the works of [17, 33]. An example of differential equations is tested to ensure the validity of the abstract results.

scholarly journals A note on C. C. Yang's question corresponding to linear shift operator.

2021 ◽  
Vol 13(62) (2) ◽  
pp. 423-432
Author(s):  
Abhijit Banerjee ◽  
Arpita Roy
Keyword(s):  
Meromorphic Functions ◽  
Shift Operator ◽  
Future Research ◽  
Shared Value ◽  
Shift Operators

In this paper, we investigate shared value problems of finite ordered meromorphic functions with the linear shift operators governed by them, which practically provide an answer to Yang’s question. We exhibit a number of examples which will justify some assertions in the paper. Based on some examples relevant with the discussion, we also place a question in the penultimate section for future research.

scholarly journals Entire functions of restricted hyper-order sharing a set of two small functions IM with their linear c-shift operators

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abhijit Banerjee ◽  
Arpita Roy
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Shift Operator ◽  
Research Work ◽  
Original Research ◽  
Exponent Of Convergence ◽  
Content Type ◽  
Shift Operators ◽  
Small Functions ◽  
Hyper Order

PurposeThe paper aims to build the relationship between an entire function of restricted hyper-order with its linear c-shift operator.Design/methodology/approachStandard methodology for papers in difference and shift operators and value distribution theory have been used.FindingsThe relation between an entire function of restricted hyper-order with its linear c-shift operator was found under the periphery of sharing a set of two small functions IM (ignoring multiplicities) when exponent of convergence of zeros is strictly less than its order. This research work is an improvement and extension of two previous papers.Originality/valueThis is an original research work.

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