Shift operator techniques for the classification of multipole‐phonon states. V. Properties of shift operators in the R(7) group

1980 ◽  
Vol 21 (8) ◽  
pp. 1973-1976 ◽  
Author(s):  
H. E. De Meyer ◽  
G. Vanden Berghe
Keyword(s):  
Shift Operator ◽  
Shift Operators

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.

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 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.

scholarly journals On t-entropy and variational principle for the spectral radius of weighted shift operators

2009 ◽  
Vol 30 (5) ◽  
pp. 1331-1342 ◽  
Author(s):  
V. I. BAKHTIN
Keyword(s):  
Dynamical System ◽  
Variational Principle ◽  
Spectral Radius ◽  
Shift Operator ◽  
Weighted Shift ◽  
Topological Pressure ◽  
Weighted Shift Operator ◽  
Shift Operators ◽  
Dual Functional ◽  
Discrete Time Dynamical Systems

AbstractIn this paper we introduce a new functional invariant of discrete time dynamical systems—the so-called t-entropy. The main result is that this t-entropy is the Legendre dual functional to the logarithm of the spectral radius of the weighted shift operator on L1(X,m) generated by the dynamical system. This result is called the variational principle and is similar to the classical variational principle for the topological pressure.

scholarly journals Uniqueness of meromorphic functions with their reduced linear c-shift operators sharing two or more values or sets

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Abhijit Banerjee ◽  
Saikat Bhattacharyya
Keyword(s):  
Complex Plane ◽  
Meromorphic Functions ◽  
Shift Operator ◽  
Future Research ◽  
Weighted Sharing ◽  
Shift Operators ◽  
Extended Complex ◽  
Open Question ◽  
Extended Complex Plane

AbstractIn the paper, we introduce a new notion of reduced linear c-shift operator $L _{c}^{r}\,f$Lcrf, and with the aid of this new operator, we study the uniqueness of meromorphic functions $f(z)$f(z) and $L_{c}^{r}\,f$Lcrf sharing two or more values in the extended complex plane. The results obtained in the paper significantly improve a number of existing results. Further, using the notion of weighted sharing of sets, we deal the same problem. We exhibit a handful number of examples to justify certain statements relevant to the content of the paper. We are also able to determine the form of the function that coincides with its reduced linear c-shift operator. At the end of the paper, we pose an open question for future research.

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