A Spectral Characterization of Exponentially Dichotomic and Hyperbolic Evolution Families
نویسنده
چکیده
We characterize hyperbolic evolution families on a Banach space X by means of spectral properties of the induced semigroup on the spaces C 0 (IR; X) and L p 1. Exponentially dichotomic and hyperbolic evolution families Given a non{autonomous Cauchy problem _ u(t) = A(t)u(t); u(s) = x s 2 X ; t s 2 IR; (nCP) on a Banach space X with possibly unbounded operators A(t), t 2 IR, on X, the solutions of (nCP) lead (under certain conditions) to a family (U(t; s)) ts in the space L(X) of bounded linear operators on X, satisfying the following properties: This paper is part of a research project supported by the Deutsche Forschungsgemeinschaft DFG.
منابع مشابه
Distribution of Periods of Closed Trajectories in Exponentially Shrinking Intervals
For hyperbolic flows over basic sets we study the asymptotic of the number of closed trajectories γ with periods Tγ lying in exponentially shrinking intervals (x−e−δx, x+ e), δ > 0, x → +∞. A general result is established which concerns hyperbolic flows admitting symbolic models whose corresponding Ruelle transfer operators satisfy some spectral estimates. This result applies to a variety of hy...
متن کاملHyperbolic monopoles, JNR data and spectral curves
A large class of explicit hyperbolic monopole solutions can be obtained from JNR instanton data, if the curvature of hyperbolic space is suitably tuned. Here we provide explicit formulae for both the monopole spectral curve and its rational map in terms of JNR data. Examples with platonic symmetry are presented, together with some one-parameter families with cyclic and dihedral symmetries. Thes...
متن کاملSemi-analytical Solution for Time-dependent Creep Analysis of Rotating Cylinders Made of Anisotropic Exponentially Graded Material (EGM)
In the present paper, time dependent creep behavior of hollow circular rotating cylinders made of exponentially graded material (EGM) is investigated. Loading is composed of an internal pressure, a distributed temperature field due to steady state heat conduction with convective boundary condition and a centrifugal body force. All the material properties are assumed to be exponentially graded a...
متن کاملChebyshev Spectral Collocation Method for Computing Numerical Solution of Telegraph Equation
In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...
متن کاملDouble Integral Characterization for Bergman Spaces
‎In this paper we characterize Bergman spaces with‎ ‎respect to double integral of the functions $|f(z)‎ ‎-f(w)|/|z-w|$,‎ ‎$|f(z)‎ -‎f(w)|/rho(z,w)$ and $|f(z)‎ ‎-f(w)|/beta(z,w)$,‎ ‎where $rho$ and $beta$ are the pseudo-hyperbolic and hyperbolic metrics‎. ‎We prove some necessary and sufficient conditions that implies a function to be...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1994