Abstract
In this paper, we give a very general “isotropic” (1) Paley-Wiener(2) theorem, and a series of its applications. Among the latter: extensions of classical results like a well-known theorem on entire Laplace transforms(3) of exponential type on L2(4), far beyond allLP p ≥ 1( 5 )up to non exponentially bounded continuous functions, distributions, and further generalized functions; extension (and also brief elegant proofs) of central results on nilpotent and superstable(6) semigroups (as those of M. Krein(7), A. Sinclair, see Section 5); extension (and also brief elegant proof) of a result of F. Neubrander and S. Flory on suppfin terms of growth off (n) (λ 0 ) (∼v =L.T.) extended to the context of asymptotic Laplace transform.
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Lumer, G. (2003). A General “Isotropic” Paley-Wiener Theorem and Some of its Applications. In: Iannelli, M., Lumer, G. (eds) Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics. Progress in Nonlinear Differential Equations and Their Applications, vol 55. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8085-5_22
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DOI: https://doi.org/10.1007/978-3-0348-8085-5_22
Publisher Name: Birkhäuser, Basel
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