A maximal ergodic theorem for Abel means of continuous-parameter operator semigroups
نویسندگان
چکیده
منابع مشابه
A Maximal Theorem for Holomorphic Semigroups
This has a unique solution v(x, t) = Ttf(x) in the sense of Hille and Phillips [14, p. 622] whenever Tt is a C0–semigroup on X with generator −A; one writes Tt = e−tA [14, p. 321]. In order to ensure that v(x, t) converges μ-almost everywhere to f(x) as t→ 0+, it is often necesary to impose further conditions on f . For any closed linear operator V in X, we recall that the domain of V is the Ba...
متن کاملMean Ergodic Theorems for C0 Semigroups of Continuous Linear Operators
In this paper we obtained mean ergodic theorems for semigroups of bounded linear or continuous affine linear operators on a Banach space under non-power bounded conditions. We then apply them to the wave equation and the system of elasticity to show that the mean of their solutions converges to their equilibriums.
متن کاملEasy and nearly simultaneous proofs of the Ergodic Theorem and Maximal Ergodic Theorem
We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem. Let (X,B, μ) be a probability space, T : X → X a (possibly noninvertible) measurepreserving transformation, and f ∈ L(X,B, μ). Let
متن کاملApplication of the Mean Ergodic Theorem to Certain Semigroups
We study the asymptotic behaviour of solutions of the Cauchy problem u′ = (∑n j=1(Aj + A −1 j ) − 2nI ) u, u(0) = x as t → ∞, for invertible isometries A1, . . . , An.
متن کاملContinuous Maximal Regularity and Analytic Semigroups
In this paper we establish a result regarding the connection between continuous maximal regularity and generation of analytic semigroups on a pair of densely embedded Banach spaces. More precisely, we show that continuous maximal regularity for a closed operator A : E1 → E0 implies that A generates a strongly continuous analytic semigroup on E0 with domain equal E1.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1971
ISSN: 0022-1236
DOI: 10.1016/0022-1236(71)90044-9