Nonexistence results for relaxation spectra with compact support

R. J. Douglas, H. R. Whittle Gruffudd

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

1 Dyfyniadau(SciVal)
185 Wedi eu Llwytho i Lawr (Pure)

Crynodeb

In this paper we consider the problem of recovering the (transformed) relaxation spectrum h from the (transformed) loss modulus g by inverting the integral equation $g={\rm{sech}}\ast h$, where $\ast $ denotes convolution, using Fourier transforms. We are particularly interested in establishing properties of h, having assumed that the Fourier transform of g has entire extension to the complex plane. In the setting of square integrable functions, we demonstrate that the Paley–Wiener theorem cannot be used to show the existence of non-trivial relaxation spectra with compact support. We prove a stronger result for tempered distributions: there are no non-trivial relaxation spectra with compact support. Finally we establish necessary and sufficient conditions for the relaxation spectrum h to be strictly positive definite.
Iaith wreiddiolSaesneg
Rhif yr erthygl035006
Tudalennau (o-i)1-13
Nifer y tudalennau13
CyfnodolynInverse Problems
Cyfrol32
Rhif cyhoeddi3
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - 19 Chwef 2016

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