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Analytic semigroups in Banach algebras and a theorem of Hille

Tadeusz Pytlik (1987)

Colloquium Mathematicae

Analytic semigroups on vector valued noncommutative $L^{p}$ -spaces

Cédric Arhancet (2013)

Studia Mathematica

We give sufficient conditions on an operator space E and on a semigroup of operators on a von Neumann algebra M to obtain a bounded analytic or R-analytic semigroup ( ${(T \otimes I d_{E})}_{t \geq 0}$ on the vector valued noncommutative $L^{p}$ -space $L^{p} (M, E)$ . Moreover, we give applications to the $H^{\infty} (Σ_{θ})$ functional calculus of the generators of these semigroups, generalizing some earlier work of M. Junge, C. Le Merdy and Q. Xu.

Analytic vectors and generation of one-parameter groups

Jan Rusinek (1984)

Studia Mathematica

Analyticity of the propagators of second order linear differential equations in Banach spaces.

T. Xio, J. Liang (1992)

Semigroup forum

Analytische Vektoren von Faltungshalbgruppen. I.

Thomas Drisch, Wilfried Hazod (1980)

Mathematische Zeitschrift

Approximate solution of an inhomogeneous abstract differential equation

Emil Vitásek (2012)

Applications of Mathematics

Recently, we have developed the necessary and sufficient conditions under which a rational function $F (h A)$ approximates the semigroup of operators $exp (t A)$ generated by an infinitesimal operator $A$ . The present paper extends these results to an inhomogeneous equation $u^{'} (t) = A u (t) + f (t)$ .

Approximate solutions of abstract differential equations

Emil Vitásek (2007)

Applications of Mathematics

The methods of arbitrarily high orders of accuracy for the solution of an abstract ordinary differential equation are studied. The right-hand side of the differential equation under investigation contains an unbounded operator which is an infinitesimal generator of a strongly continuous semigroup of operators. Necessary and sufficient conditions are found for a rational function to approximate the given semigroup with high accuracy.