Equiconvergence theorems for Chébli-Trimèche hypergroups
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 2, pp. 211-265.

We consider a Sturm-Liouville operator of the kind d 2 dt 2 +A ' t Atd dt on 0,+ and the related eigenfunction expansion. We prove that, under suitable assumptions on At, the partial sums of the Fourier integral associated to such expansion behave like the partial sums of the classical Fourier-Bessel transform. This implies an almost everywhere convergence result for L p Atdt functions. Our methods rely on asymptotic expansions for the eigenfunctions and the Harish-Chandra function that we prove under very weak hypotheses.

Classification : 43A62,  43A32,  34L10
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     author = {Brandolini, Luca and Gigante, Giacomo},
     title = {Equiconvergence theorems for {Ch\'ebli-Trim\`eche} hypergroups},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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     publisher = {Scuola Normale Superiore, Pisa},
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Brandolini, Luca; Gigante, Giacomo. Equiconvergence theorems for Chébli-Trimèche hypergroups. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 2, pp. 211-265. http://www.numdam.org/item/ASNSP_2009_5_8_2_211_0/

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