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• W2912201613 abstract "We establish a positive product formula for the solutions of the Sturm-Liouville equation $ell(u) = lambda u$, where $ell$ belongs to a general class which includes singular and degenerate Sturm-Liouville operators. Our technique relies on a positivity theorem for possibly degenerate hyperbolic Cauchy problems and on a regularization method which makes use of the properties of the diffusion semigroup generated by the Sturm-Liouville operator. We show that the product formula gives rise to a convolution algebra structure on the space of finite measures, and we discuss whether this structure satisfies the basic axioms of the theory of hypergroups. We introduce the notion of a degenerate hypergroup of full support and improve the known existence theorems for Sturm-Liouville hypergroups. Convolution-type integral equations on weighted Lebesgue spaces are also introduced, and a solvability condition is established." @default.
• W2912201613 created "2019-02-21" @default.
• W2912201613 creator A5024798937 @default.
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• W2912201613 date "2019-01-30" @default.
• W2912201613 modified "2023-09-27" @default.
• W2912201613 title "Sturm-Liouville hypergroups without the compactness axiom" @default.
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• W2912201613 hasPublicationYear "2019" @default.
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