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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.

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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References

1Chen, G. and Russell, D. L.. A mathematical model for linear elastic systems with structural damping (Mathematics Research Center, University of Wisconsin-Madison: Technical Summary Report 2089, 1980).Google Scholar
2Hille, E.. Functional Analysis and Semi-Groups (New York: American Mathematical Society, 1948).Google Scholar
3Ho, L. F. and Russell, D. L.. Admissible input elements for systems in Hilbert space and aCarleson measure criterion. SIAM J. Control Optim. 21 (1983), 614–639.CrossRefGoogle Scholar
4Rebarber, R.. Canonical forms for a class of distributed parameter control systems (preprint).Google Scholar
5Rebarber, R.. A class of meromorphic functions used for spectral determination (preprint).Google Scholar
6Riesz, F. and Nagy, B. Sz.. Functional Analysis (New York: FrederickUngar, 1955).Google Scholar
7Rudin, W.. Real and Complex Analysis (New York: McGraw-Hill, 1966).Google Scholar
8Russell, D. L.. Uniform bases of exponentials, neutral groups and a transform theory for Hm[a, b]. (Mathematics Research Center, University of Wisconsin-Madison: Technical Summary Report 2149, 1979).Google Scholar
9Russell, D. L.. Closed loop eigenvalue specification for infinite dimensional systems: augmented anddeficient hyperbolic cases. (Mathematics Research Center, University of Wisconsin-Madison: Technical Summary Report 2021, 1980).Google Scholar
10Russell, D. L.. Dual Paley–Weiner spaces and regular nonharmonic Fourier series (preprint).Google Scholar
11Russell, D.L.. Mathematical models for the elastic beam and their control theoretic implications (preprint).Google Scholar
12Salamon, D.. Control and Observation of Neutral Systems (Boston: Pitman, 1984).Google Scholar