C-Semigroups and the Cauchy Problem
نویسندگان
چکیده
منابع مشابه
Integrated Semigroups and Their Applications to the Abstract Cauchy Problem
This paper is concerned with characterizations of those linear, closed, but not necessarily densely defined operators A on a Banach space E with nonempty resolvent set for which the abstract Cauchy problem u'(t) = Au(t), u(0) = x has unique, exponentially bounded solutions for every initial value x e D(A). Investigating these operators we are led to the class of "integrated semigroups". Among o...
متن کاملThe Cauchy-davenport Theorem for Semigroups
We generalize the Davenport transform to prove that, for A = (A,+) a cancellative unital semigroup and X,Y subsets of A such that the smallest subsemigroup generated by Y is commutative, one has that |X + Y | ≥ Ω(X,Y ) := min ( |X|+ |Y | − 1, sup y0∈Y× min y∈Y \{y0} ord(y − y0) ) if 2 ≤ |X|, |Y | < ∞. While extending the Cauchy-Davenport theorem to the broader and abstract setting of (possibly ...
متن کاملDifferentiability of convolutions, integrated semigroups of bounded semi-variation, and the inhomogeneous Cauchy problem
If T = {T (t); t ≥ 0} is a strongly continuous family of bounded linear operators between two Banach spaces X and Y and f ∈ L1(0, b, X), the convolution of T with f is defined by (T ∗f)(t) = ∫ t 0 T (s)f(t− s)ds. It is shown that T ∗ f is continuously differentiable for all f ∈ C(0, b, X) if and only if T is of bounded semi-variation on [0, b]. Further T ∗ f is continuously differentiable for a...
متن کاملEvolution Semigroups for Nonautonomous Cauchy Problems
In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems (NCP ) { u̇(t) = A(t)u(t) u(s) = x ∈ X on a Banach space X by the existence of certain evolution semigroups. Then, we use these generation results for evolution semigroups to derive wellposedness for nonautonomous Cauchy problems under some “concrete” conditions. As a typical example, we discuss the so called “...
متن کاملThe Cauchy Process and the Steklov Problem
Let Xt be a Cauchy process in R, d ≥ 1. We investigate some of the fine spectral theoretic properties of the semigroup of this process killed upon leaving a domain D. We establish a connection between the semigroup of this process and a mixed boundary value problem for the Laplacian in one dimension higher, known as the “Mixed Steklov Problem.” Using this we derive a variational characterizatio...
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: 1993
ISSN: 0022-1236
DOI: 10.1006/jfan.1993.1003