scholarly journals A SHORT NOTE ON THE FRAME SET OF ODD FUNCTIONS

2018 ◽  
Vol 98 (3) ◽  
pp. 481-493 ◽  
Author(s):  
MARKUS FAULHUBER
Keyword(s):  
Wigner Distribution ◽  
Short Note ◽  
Gabor Frame ◽  
Gabor Frames ◽  
Simple Argument ◽  
Gabor Systems ◽  
One Dimensional ◽  
Separable Case ◽  
The One ◽  
Frame Set

We give a simple argument which shows that Gabor systems consisting of odd functions of$d$variables and symplectic lattices of density$2^{d}$cannot constitute a Gabor frame. In the one-dimensional, separable case, this follows from a more general result of Lyubarskii and Nes [‘Gabor frames with rational density’,Appl. Comput. Harmon. Anal.34(3) (2013), 488–494]. We use a different approach exploiting the algebraic relation between the ambiguity function and the Wigner distribution as well as their relation given by the (symplectic) Fourier transform. Also, we do not need the assumption that the lattice is separable and, hence, new restrictions are added to the full frame set of odd functions.

FINITE SYSTEMS ON PHASE SPACE

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1956-1967 ◽  
Author(s):  
KURT BERNARDO WOLF
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Hamiltonian Systems ◽  
Wigner Distribution ◽  
Wigner Distribution Function ◽  
Finite Fourier Transform ◽  
One Dimensional ◽  
Finite Systems ◽  
The One ◽  
Definition Of

This contribution summarizes work on finite, non-cyclic Hamiltonian systems —in particular the one-dimensional finite oscillator—, in conjunction with a Lie algebraic definition of the (meta-) phase space of finite systems, and a corresponding Wigner distribution function for the state vectors. The consistency of this approach is important for the strategy of fractionalization of a finite Fourier transform, and the contraction of finite unitary to continuous symplectic transformations of Hamiltonian systems.

Partial Gabor frames and dual frames

2021 ◽  
pp. 2150035
Author(s):  
Yu Tian ◽  
Hui-Fang Jia ◽  
Guo-Liang He
Keyword(s):  
Density Theorem ◽  
Gabor Frame ◽  
Gabor Frames ◽  
Dual Frame ◽  
Gabor System ◽  
Dual Frames ◽  
Gabor Systems

The theory of Gabor frames has been extensively investigated. This paper addresses partial Gabor systems. We introduce the concepts of partial Gabor system, frame and dual frame. We present some conditions for a partial Gabor system to be a partial Gabor frame, and using these conditions, we characterize partial dual frames. We also give some examples. It is noteworthy that the density theorem does not hold for general partial Gabor systems.

RATIONAL TIME-FREQUENCY GABOR FRAMES ASSOCIATED WITH PERIODIC SUBSETS OF THE REAL LINE

2014 ◽  
Vol 12 (02) ◽  
pp. 1450013 ◽  
Author(s):  
JEAN-PIERRE GABARDO ◽  
YUN-ZHANG LI
Keyword(s):  
Positive Measure ◽  
Measurable Subset ◽  
Gabor Frame ◽  
Gabor Frames ◽  
Type I ◽  
Type Ii ◽  
Zak Transform ◽  
Gabor System ◽  
Gabor Systems ◽  
Time Frequency

For a, b > 0 and g ∈ L2(ℝ), write 𝒢(g, a, b) for the Gabor system: [Formula: see text] Let S be an aℤ-periodic measurable subset of ℝ with positive measure. It is well-known that the projection 𝒢(gχS, a, b) of a frame 𝒢(g, a, b) in L2(ℝ) onto L2(S) is a frame for L2(S). However, when ab > 1 and S ≠ ℝ, 𝒢(g, a, b) cannot be a frame in L2(ℝ) for any g ∈ L2(ℝ), while it is possible that there exists some g such that 𝒢(g, a, b) is a frame for L2(S). So the projections of Gabor frames in L2(ℝ) onto L2(S) cannot cover all Gabor frames in L2(S). This paper considers Gabor systems in L2(S). In order to use the Zak transform, we only consider the case where the product ab is a rational number. With the help of a suitable Zak transform matrix, we characterize Gabor frames for L2(S) of the form 𝒢(g, a, b), and obtain an expression for the canonical dual of a Gabor frame. We also characterize the uniqueness of Gabor duals of type I (respectively, type II).

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Adiabatic large polarons in anisotropic molecular crystals

2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj
Keyword(s):  
Energy Transfer ◽  
Effective Mass ◽  
Molecular Crystals ◽  
Single Chain ◽  
Proper Understanding ◽  
One Dimensional ◽  
Interchain Coupling ◽  
Large Polaron ◽  
The One

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.

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