منابع مشابه
Mean 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 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 کاملResearch Article Nonlinear Mean Ergodic Theorems for Semigroups inHilbert Spaces
Let K be a nonempty subset of a Hilbert space , where K is not necessarily closed and convex. A family Γ= {T(t); t ≥ 0} of mappings T(t) is called a semigroup on K if (S1) T(t) is a mapping from K into itself for t ≥ 0, (S2) T(0)x = x and T(t+ s)x = T(t)T(s)x for x ∈ K and t,s≥ 0, (S3) for each x ∈ K , T(·)x is strongly measurable and bounded on every bounded subinterval of [0,∞). Let Γ be a se...
متن کاملErgodic Theory for C-semigroups
We deene the ergodicity of C-semigroups in this paper, and then characterize the generators.
متن کاملSemigroups of Linear Operators
Our goal is to define exponentials of linear operators. We will try to construct etA as a linear operator, where A : D(A)→ X is a general linear operator, not necessarily bounded. Notationally, it seems like we are looking for a solution to μ̇(t) = Aμ(t), μ(0) = μ0, and we would like to write μ(t) = eμ0. It turns out that this will hold once we make sense of the terms. How can we construct etA w...
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: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
سال: 2011
ISSN: 1578-7303,1579-1505
DOI: 10.1007/s13398-011-0054-2