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The Application of Special Transform Methods derived from the Laplace Transform
Meccanica, 1997The present note discusses the \(\delta\)-transform, the \(d\alpha\)-transform and the Laplace transform. The relationship between a Laplace transformed function \(L[x]= X(s)\) and the \(\delta\)-transformed function \(X_\delta(s)\) as well as between the \(z\)-transform and the \(\delta\)-transform is discussed.
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Laplace Transform Methods for Evolution Equations
1977The evolution equations considered here are of the form (1) u’(t) = A(t)u(t) + f(t), t > 0 ; u(0) = u0. The given function f and the unknown function u take values in a complex Banach space X, and the initial condition u0 is in X. The A(t) are closed linear operators with domains dense in X. The time independent case is the case A(t) ≡ A.
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