Integrated semigroups of unbounded linear operators -- Cauchy problem. II.
Kravarušić, Ratko, Mijatović, Milorad, Pilipović, Stevan (1998)
Novi Sad Journal of Mathematics
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Kravarušić, Ratko, Mijatović, Milorad, Pilipović, Stevan (1998)
Novi Sad Journal of Mathematics
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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...
Piotr Budzyński, Jan Stochel (2007)
Studia Mathematica
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Joint subnormality of a family of composition operators on L²-space is characterized by means of positive definiteness of appropriate Radon-Nikodym derivatives. Next, simplified positive definiteness conditions guaranteeing joint subnormality of a C₀-semigroup of composition operators are supplied. Finally, the Radon-Nikodym derivatives associated to a jointly subnormal C₀-semigroup of composition operators are shown to be the Laplace transforms of probability measures (modulo a C₀-group...
E. Pap, S. Pilipović (1979)
Matematički Vesnik
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S. Bjon (1994)
Semigroup forum
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Oleg V. Davydov (1993)
Manuscripta mathematica
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N. Sauer, J.E. Singleton (1989)
Semigroup forum
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J.M.A.M. van Neerven (1991)
Semigroup forum
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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....
Markin, Marat V. (2002)
International Journal of Mathematics and Mathematical Sciences
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Janfada, Mohammad (2009)
Abstract and Applied Analysis
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Milorad Mijatović, Stevan Pilipović (1997)
Matematički Vesnik
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Bogdanović, Stojan, Imreh, Balázs (1999)
Novi Sad Journal of Mathematics
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