scholarly journals On the translation invariance of wavelet subspaces

2000 ◽  
Vol 6 (5) ◽  
pp. 551-558 ◽  
Author(s):  
Eric Weber
Keyword(s):  
Translation Invariance ◽  
Wavelet Subspaces

Translation invariance and the problem of the bipolaron

1998 ◽  
Vol 168 (4) ◽  
pp. 465 ◽  
Author(s):  
Viktor D. Lakhno
Keyword(s):  
Translation Invariance

scholarly journals Discrete Nonlinear Schrödinger Systems for Periodic Media with Nonlocal Nonlinearity: The Case of Nematic Liquid Crystals

2021 ◽  
Vol 11 (10) ◽  
pp. 4420
Author(s):  
Panayotis Panayotaros
Keyword(s):  
Differential Equation ◽  
Infinite System ◽  
Linear Part ◽  
Optical Power ◽  
Explicit Construction ◽  
Translation Invariance ◽  
Nonlocal Nonlinearity ◽  
Wannier Functions ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger Systems

We study properties of an infinite system of discrete nonlinear Schrödinger equations that is equivalent to a coupled Schrödinger-elliptic differential equation with periodic coefficients. The differential equation was derived as a model for laser beam propagation in optical waveguide arrays in a nematic liquid crystal substrate and can be relevant to related systems with nonlocal nonlinearities. The infinite system is obtained by expanding the relevant physical quantities in a Wannier function basis associated to a periodic Schrödinger operator appearing in the problem. We show that the model can describe stable beams, and we estimate the optical power at different length scales. The main result of the paper is the Hamiltonian structure of the infinite system, assuming that the Wannier functions are real. We also give an explicit construction of real Wannier functions, and examine translation invariance properties of the linear part of the system in the Wannier basis.

scholarly journals PHASE TRANSITIONS AND QUANTUM STABILIZATION IN QUANTUM ANHARMONIC CRYSTALS

2008 ◽  
Vol 20 (05) ◽  
pp. 529-595 ◽  
Author(s):  
ALINA KARGOL ◽  
YURI KONDRATIEV ◽  
YURI KOZITSKY
Keyword(s):  
Phase Transitions ◽  
Gibbs Measures ◽  
Quantum Effects ◽  
Gibbs States ◽  
Translation Invariance ◽  
Unified Theory ◽  
The Relationship ◽  
Anharmonic Crystals

A unified theory of phase transitions and quantum effects in quantum anharmonic crystals is presented. In its framework, the relationship between these two phenomena is analyzed. The theory is based on the representation of the model Gibbs states in terms of path measures (Euclidean Gibbs measures). It covers the case of crystals without translation invariance, as well as the case of asymmetric anharmonic potentials. The results obtained are compared with those known in the literature.

Fractional convolution, fractional correlation and their translation invariance properties

2010 ◽  
Vol 90 (6) ◽  
pp. 1976-1984 ◽  
Author(s):  
Rafael Torres ◽  
Pierre Pellat-Finet ◽  
Yezid Torres
Keyword(s):  
Translation Invariance ◽  
Invariance Properties

A sampling theorem for wavelet subspaces

1992 ◽  
Vol 38 (2) ◽  
pp. 881-884 ◽  
Author(s):  
G.G. Walter
Keyword(s):  
Sampling Theorem ◽  
Wavelet Subspaces

Generalized average sampling and reconstruction for wavelet subspaces

2018 ◽  
Vol 26 (2) ◽  
pp. 333-342
Author(s):  
S. Yugesh ◽  
P. Devaraj
Keyword(s):  
Average Sampling ◽  
Wavelet Subspaces ◽  
Sampling And Reconstruction

Translation Invariance

2019 ◽  
pp. 39-45
Author(s):  
Patrick Schultz ◽  
David I. Spivak
Keyword(s):  
Translation Invariance
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