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A Laplace transform relevant to holomorphic semigroups

Published online by Cambridge University Press:  14 November 2011

R.L. Rebarber
R.L. Rebarber
Affiliation:
Department of Mathematics and Statistics, University of Nebraska, Lincoln, Nebraska 68502, U.S.A.
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Synopsis

A Laplace transform is developed for functions which are holomorphic in the complex wedge Ω = {z| |arg (z)| < σ}, where 0 ≦ σ < π. The resulting transform will be holomorphic in a complementary wedge of the form Ωa = {a+ z||arg (z)|< (π/2) +σ for some a. This Laplace transform is shown to be an isomorphism between two appropriate spaces. The spanning properties of sets of the form {eλkS}k∊I in the domain space are studied. These results are then applied to a control problem.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 105 , Issue 1 , 1987 , pp. 243 - 258
Copyright
Copyright © Royal Society of Edinburgh 1987

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