scholarly journals A Desch–Schappacher perturbation theorem for bi‐continuous semigroups

2020 ◽  
Vol 293 (6) ◽  
pp. 1053-1073
Author(s):  
Christian Budde ◽  
Bálint Farkas
Keyword(s):  
Perturbation Theorem

ON THE THEORY OF THE DOPPLER EFFECT IN A MOVING MEDIUM

1998 ◽  
Vol 13 (01) ◽  
pp. 1-6 ◽  
Author(s):  
BRUNO BERTOTTI
Keyword(s):  
Solar Wind ◽  
Doppler Effect ◽  
Dispersive Medium ◽  
Time Derivative ◽  
Optical Path ◽  
Moving Medium ◽  
Perturbation Theorem ◽  
Hamiltonian Theory ◽  
The Doppler Effect ◽  
Definition Of

The increase in the accuracy of Doppler measurements in space requires a rigorous definition of the observed quantity when the propagation occurs in a moving, and possibly dispersive medium, like the solar wind. This is usually done in two divergent ways: in the phase viewpoint it is the time derivative of the correction to the optical path; in the ray viewpoint the signal is obtained form the deflection produced in the ray. They can be reconciled by using the time derivative of the optical path in the Lagrangian sense, i.e. differentiating from ray to ray. To rigorously derive this result an understanding, through relativistic Hamiltonian theory, of the delicate interplay between rays and phase is required; a general perturbation theorem which generalizes the concept of the Doppler effect as a Lagrangian derivative is proved. Relativistic retardation corrections O(v) are obtained, well within the expected sensitivity of Doppler experiments near solar conjunction.

A perturbation method and the limit-point case of even order symmetric differential expressions

1983 ◽  
Vol 94 (1-2) ◽  
pp. 121-135 ◽  
Author(s):  
Bernhard Mergler ◽  
Bernd Schultze
Keyword(s):  
Perturbation Method ◽  
Fourth Order ◽  
Limit Point ◽  
Perturbation Theorem ◽  
Order Case ◽  
Even Order ◽  
Limit Point Case ◽  
New Perturbation ◽  
Bounded Perturbations

SynopsisWe give a new perturbation theorem for symmetric differential expressions (relatively bounded perturbations, with relative bound 1) and prove with this theorem a new limit-point criterion generalizing earlier results of Schultze. We also obtain some new results in the fourth-order case.

On the principle of exchange of stabilities

1969 ◽  
Vol 310 (1502) ◽  
pp. 341-358 ◽  
Keyword(s):  
Growth Rate ◽  
Couette Flow ◽  
Equations Of State ◽  
Travelling Waves ◽  
Time Dependent ◽  
Heat Sources ◽  
Constant Heat ◽  
Perturbation Theorem ◽  
Adjoint Operators ◽  
Real Self

A perturbation theorem is proved: a class of real, bounded (non-self-adjoint) perturbations of norm ϵ to real self-adjoint operators preserve the reality of the simple eigenvalues for ϵ sufficiently small. A bound is obtained on ϵ. Application is made to Bénard convection with constant heat sources, radiation, particular time-dependent profiles and nonlinear equations of state and to instability of circular Couette flow for a range of gap widths. In each case the growth rate is the eigenvalue and hence if ϵ < ϵ c , travelling waves (either growing or decaying) are forbidden.

A perturbation theorem for the equation −Δu + λu = uP in unbounded domains

1997 ◽  
Vol 28 (11) ◽  
pp. 1867-1877 ◽  
Author(s):  
Andrea Dall'aglio ◽  
Massimo Grossi
Keyword(s):  
Unbounded Domains ◽  
Perturbation Theorem

The homological hexagonal lemma

2018 ◽  
Vol 25 (4) ◽  
pp. 603-622
Author(s):  
Francis Sergeraert
Keyword(s):  
Vector Fields ◽  
The Other ◽  
Perturbation Theorem ◽  
Other Hand ◽  
Global Understanding ◽  
The One ◽  
Homological Perturbation

Abstract We propose in this article a global understanding of, on the one hand, the homological perturbation theorem (HPT) and, on the other hand, of Robin Forman’s theorems about the discrete vector fields (DVFs). Forman’s theorems become a simple and clear consequence of the HPT. Above both subjects, the homological hexagonal lemma quite elementary.

scholarly journals Lyapunov optimization for non-generic one-dimensional expanding Markov maps

2019 ◽  
Vol 40 (9) ◽  
pp. 2571-2592 ◽  
Author(s):  
MAO SHINODA ◽  
HIROKI TAKAHASI
Keyword(s):  
Periodic Orbit ◽  
Finite Number ◽  
Dense Subset ◽  
Equilibrium States ◽  
Positive Entropy ◽  
Hölder Continuous ◽  
Perturbation Theorem ◽  
One Dimensional ◽  
Lyapunov Optimization ◽  
Shift Map

For a non-generic, yet dense subset of$C^{1}$expanding Markov maps of the interval we prove the existence of uncountably many Lyapunov optimizing measures which are ergodic, fully supported and have positive entropy. These measures are equilibrium states for some Hölder continuous potentials. We also prove the existence of another non-generic dense subset for which the optimizing measure is unique and supported on a periodic orbit. A key ingredient is a new$C^{1}$perturbation theorem which allows us to interpolate between expanding Markov maps and the shift map on a finite number of symbols.

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