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Displaying similar documents to “A sequential theory of some semigroups in special spaces of generalized functions”

Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces, II

Piotr Budzyński, Jan Stochel (2009)

Studia Mathematica

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In the previous paper, we have characterized (joint) subnormality of a C₀-semigroup of composition operators on L²-space by positive definiteness of the Radon-Nikodym derivatives attached to it at each rational point. In the present paper, we show that in the case of C₀-groups of composition operators on L²-space the positive definiteness requirement can be replaced by a kind of consistency condition which seems to be simpler to work with. It turns out that the consistency condition...

Decomposing and twisting bisectorial operators

Wolfgang Arendt, Alessandro Zamboni (2010)

Studia Mathematica

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Bisectorial operators play an important role since exactly these operators lead to a well-posed equation u'(t) = Au(t) on the entire line. The simplest example of a bisectorial operator A is obtained by taking the direct sum of an invertible generator of a bounded holomorphic semigroup and the negative of such an operator. Our main result shows that each bisectorial operator A is of this form, if we allow a more general notion of direct sum defined by an unbounded closed projection....