Generalized shift operators and pseudo-polynomials of fractional order

2003 ◽  
Vol 141 (1) ◽  
pp. 215-224 ◽  
Author(s):  
G Dattoli ◽  
P.E Ricci ◽  
D Sacchetti
Keyword(s):  
Fractional Order ◽  
Shift Operators ◽  
Generalized Shift

Weighted generalized shift operators on $$\ell ^p$$ spaces

2021 ◽  
Author(s):  
Fatemah Ayatollah Zadeh Shirazi ◽  
Fatemeh Ebrahimifar ◽  
Reza Rezavand
Keyword(s):  
Shift Operators ◽  
Generalized Shift

Reconstruction of stationary and non-stationary signals by the generalized Prony method

2019 ◽  
Vol 17 (02) ◽  
pp. 179-210 ◽  
Author(s):  
Gerlind Plonka ◽  
Kilian Stampfer ◽  
Ingeborg Keller
Keyword(s):  
Linear Operators ◽  
Sparse Signal ◽  
Hyperbolic Functions ◽  
Shift Operators ◽  
Sparse Polynomial ◽  
Prony Method ◽  
Stationary Signals ◽  
Generalized Shift ◽  
Phase Functions ◽  
Polynomial Expansions

We employ the generalized Prony method in [T. Peter and G. Plonka, A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators, Inverse Problems 29 (2013) 025001] to derive new reconstruction schemes for a variety of sparse signal models using only a small number of signal measurements. By introducing generalized shift operators, we study the recovery of sparse trigonometric and hyperbolic functions as well as sparse expansions into Gaussians chirps and modulated Gaussian windows. Furthermore, we show how to reconstruct sparse polynomial expansions and sparse non-stationary signals with structured phase functions.

ON A FAMILY OF GENERALIZED SHIFT OPERATORS

1977 ◽  
Vol 11 (4) ◽  
pp. 865-888 ◽  
Author(s):  
R J Grabovskaja ◽  
V I Kononenko ◽  
V B Osipov
Keyword(s):  
Shift Operators ◽  
Generalized Shift
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