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THE COMPLEX INVERSION FORMULA REVISITED

Part of: Abstract harmonic analysis Groups and semigroups of linear operators, their generalizations and applications General theory of linear operators Integral transforms, operational calculus Differential equations in abstract spaces

Published online by Cambridge University Press:  01 February 2008

MARKUS HAASE
MARKUS HAASE*
Affiliation:
Delft Institute of Applied Analysis, TU Delft, PO Box 5031, 2600 GA Delft, The Netherlands (email: m.h.a.haase@tudelft.nl)
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Abstract

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We give a simplified proof of the complex inversion formula for semigroups and, more generally, solution families for scalar-type Volterra equations, including the stronger versions on unconditional martingale differences (UMD) spaces. Our approach is based on (elementary) Fourier analysis.

Keywords

C0 semigroupintegrated semigroupUMD spacecomplex inversionLaplace transformVolterra equation

MSC classification

Secondary: 34G10: Linear equations 43A50: Convergence of Fourier series and of inverse transforms 44A10: Laplace transform 47A60: Functional calculus 47D03: Groups and semigroups of linear operators 47D06: One-parameter semigroups and linear evolution equations 47D09: Operator sine and cosine functions and higher-order Cauchy problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 1 , February 2008 , pp. 73 - 83
Copyright
Copyright © 2008 Australian Mathematical Society

References

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