In this chapter, a very interesting theorem, due to Chernoff [4], is proven and some of its appli... more In this chapter, a very interesting theorem, due to Chernoff [4], is proven and some of its applications, viz. the Trotter-Kato Product Formula, the Feynman-Kac Formula and the Central Limit Theorem are given.
In this chapter we continue the study of \(C_0\)-semigroups concentrating on contractive and holo... more In this chapter we continue the study of \(C_0\)-semigroups concentrating on contractive and holomorphic semigroups.
This chapter is mostly of a preliminary nature. In the first section we collect results on measur... more This chapter is mostly of a preliminary nature. In the first section we collect results on measurability and integrability of vector-valued functions that will be useful throughout.
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2020
It is shown that if a Quantum Markov semigroup is “multiplicatively” perturbed under suitable con... more It is shown that if a Quantum Markov semigroup is “multiplicatively” perturbed under suitable conditions, the resulting minimal semigroup remains Markov (or conservative).
We study quasi-hyperbolicity of the delay semigroup associated with the equation u′(t)=Bu(t)+Φut,... more We study quasi-hyperbolicity of the delay semigroup associated with the equation u′(t)=Bu(t)+Φut, where ut is the history function and (B,D(B)) is the generator of a quasi-hyperbolic semigroup. We give conditions under which the associated solution semigroup of this equation generates a quasi-hyperbolic semigroup.
... Page 2. Laplace Transforms, Non-Analytic Growth Bounds and C0-Semigroups Sachi Srivastava St.... more ... Page 2. Laplace Transforms, Non-Analytic Growth Bounds and C0-Semigroups Sachi Srivastava St. ... over the last few years. Without his help this work would not have been possible. I would also like to thank Ralph Chill for some valuable discussions concerning my work. ...
In this chapter, a very interesting theorem, due to Chernoff [4], is proven and some of its appli... more In this chapter, a very interesting theorem, due to Chernoff [4], is proven and some of its applications, viz. the Trotter-Kato Product Formula, the Feynman-Kac Formula and the Central Limit Theorem are given.
In this chapter we continue the study of \(C_0\)-semigroups concentrating on contractive and holo... more In this chapter we continue the study of \(C_0\)-semigroups concentrating on contractive and holomorphic semigroups.
This chapter is mostly of a preliminary nature. In the first section we collect results on measur... more This chapter is mostly of a preliminary nature. In the first section we collect results on measurability and integrability of vector-valued functions that will be useful throughout.
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2020
It is shown that if a Quantum Markov semigroup is “multiplicatively” perturbed under suitable con... more It is shown that if a Quantum Markov semigroup is “multiplicatively” perturbed under suitable conditions, the resulting minimal semigroup remains Markov (or conservative).
We study quasi-hyperbolicity of the delay semigroup associated with the equation u′(t)=Bu(t)+Φut,... more We study quasi-hyperbolicity of the delay semigroup associated with the equation u′(t)=Bu(t)+Φut, where ut is the history function and (B,D(B)) is the generator of a quasi-hyperbolic semigroup. We give conditions under which the associated solution semigroup of this equation generates a quasi-hyperbolic semigroup.
... Page 2. Laplace Transforms, Non-Analytic Growth Bounds and C0-Semigroups Sachi Srivastava St.... more ... Page 2. Laplace Transforms, Non-Analytic Growth Bounds and C0-Semigroups Sachi Srivastava St. ... over the last few years. Without his help this work would not have been possible. I would also like to thank Ralph Chill for some valuable discussions concerning my work. ...
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