Renewal Theorems for Singular Differential Operators |
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| Authors: | Léonard Gallardo Khalifa Trimèche |
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| Affiliation: | (1) Faculté des Sciences et Techniques Département de Mathématiques, Université de Tours, Parc de Grandmont, 37200 Tours, France;(2) Département de Mathématiques, Campus Universitaire, Faculté des Sciences de Tunis, 1060 c[Tunis, Tunisie |
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| Abstract: | Let * be the convolution on M( +) associated with a second order singular differential operator L on ]0, + [. If  is a probability measure on  + with suitable moment conditions, we study how to normalize the measures *n; n  } (resp.  ) in order to get vague convergence if n + (resp. x+). The results depend on the asymptotic drift of the operator L and on a precise study of the asymptotic behaviour of its eigenfunctions. |
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| Keywords: | renewal theorems Laplace operator potential measure eigenfunctions vague convergence |
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