Periodic Operator Inspection

Opflow ◽  
2017 ◽  
Vol 43 (5) ◽  
pp. 2-2
Author(s):  
Stephen Meier
Keyword(s):  
Periodic Operator

On the spectrum of a periodic operator with a small localized perturbation

2008 ◽  
Vol 72 (4) ◽  
pp. 659-688 ◽  
Author(s):  
D I Borisov ◽  
R R Gadyl'shin
Keyword(s):  
Periodic Operator

scholarly journals The spectrum of a periodic operator with a small localized perturbation

2007 ◽  
Vol 75 (2) ◽  
pp. 255-259 ◽  
Author(s):  
D. I. Borisov ◽  
R. R. Gadyl’shin
Keyword(s):  
Periodic Operator

Bloch wave homogenisation of quasiperiodic media

2020 ◽  
pp. 1-21
Author(s):  
SISTA SIVAJI GANESH ◽  
VIVEK TEWARY
Keyword(s):  
Bloch Wave ◽  
Periodic Operator ◽  
Almost Periodic ◽  
Periodic Media ◽  
Direct Integral ◽  
Bloch Waves ◽  
Direct Integral Decomposition ◽  
Quasiperiodic Media ◽  
Integral Decomposition ◽  
Periodic Operators

Quasiperiodic media is a class of almost periodic media which is generated from periodic media through a ‘cut and project’ procedure. Quasiperiodic media displays some extraordinary optical, electronic and conductivity properties which call for the development of methods to analyse their microstructures and effective behaviour. In this paper, we develop the method of Bloch wave homogenisation for quasiperiodic media. Bloch waves are typically defined through a direct integral decomposition of periodic operators. A suitable direct integral decomposition is not available for almost periodic operators. To remedy this, we lift a quasiperiodic operator to a degenerate periodic operator in higher dimensions. Approximate Bloch waves are obtained for a regularised version of the degenerate operator. Homogenised coefficients for quasiperiodic media are obtained from the first Bloch eigenvalue of the regularised operator in the limit of regularisation parameter going to zero. A notion of quasiperiodic Bloch transform is defined and employed to obtain homogenisation limit for an equation with highly oscillating quasiperiodic coefficients.

Evolution of the complex spectrum of a periodic operator

1992 ◽  
Vol 51 (4) ◽  
pp. 396-401
Author(s):  
M. A. Pankratov
Keyword(s):  
Periodic Operator ◽  
Complex Spectrum

Zeroes of the spectral density of the periodic Schrödinger operator with Wigner–von Neumann potential

2011 ◽  
Vol 153 (1) ◽  
pp. 33-58 ◽  
Author(s):  
SERGUEI NABOKO ◽  
SERGEY SIMONOV
Keyword(s):  
Spectral Density ◽  
Continuous Spectrum ◽  
Schrödinger Operator ◽  
Bound State ◽  
Periodic Operator ◽  
Schrodinger Operator ◽  
Absolutely Continuous Spectrum ◽  
Absolutely Continuous ◽  
Von Neumann ◽  
Band Gap Structure

AbstractWe consider the Schrödinger operator α on the half-line with a periodic background potential and the Wigner–von Neumann potential of Coulomb type: csin(2ωx + δ)/(x + 1). It is known that the continuous spectrum of the operator α has the same band-gap structure as the free periodic operator, whereas in each band of the absolutely continuous spectrum there exist two points (so-called critical or resonance) where the operator α has a subordinate solution, which can be either an eigenvalue or a “half-bound” state. The phenomenon of an embedded eigenvalue is unstable under the change of the boundary condition as well as under the local change of the potential, in other words, it is not generic. We prove that in the general case the spectral density of the operator α has power-like zeroes at critical points (i.e., the absolutely continuous spectrum has pseudogaps). This phenomenon is stable in the above-mentioned sense.

scholarly journals Integrally Small Perturbations of Semigroups and Stability of Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Michael Gil'
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Evolution Equations ◽  
Periodic Operator ◽  
Stability Conditions ◽  
Partial Differential ◽  
Small Perturbations ◽  
Variable Operator ◽  
Autonomous Equation ◽  
Exponentially Stable

Let be a generator of an exponentially stable operator semigroup in a Banach space, and let   be a linear bounded variable operator. Assuming that is sufficiently small in a certain sense for the equation , we derive exponential stability conditions. Besides, we do not require that for each , the “frozen” autonomous equation is stable. In particular, we consider evolution equations with periodic operator coefficients. These results are applied to partial differential equations.

Sign in / Sign up

Export Citation Format

Share Document