On the relation between stability of continuous - and discrete - time evolution via the Cayley transform
نویسندگان
چکیده
In this paper we investigate the relation between discrete and continuous operators. More precisely, we investigate the properties of the semigroup generated by A, and the sequence Ad , n ∈ N, where Ad = (I +A)(I −A)−1. We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger results. If A is the infinitesimal generator of an analytic semigroup, then power boundedness of Ad is equivalent to the uniform boundedness of the semigroup generated by A.
منابع مشابه
On the relation between stability of continuous- and discrete-time evolution equations via the Cayley transform∗
In this paper we investigate and compare the properties of the semigroup generated by A, and the sequence Ad , n ∈ N, where Ad = (I +A)(I −A)−1. We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger results. If A is the infinitesimal generator of an analytic semigroup, the...
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