We consider a Sturm-Liouville operator of the kind on and the related eigenfunction expansion. We prove that, under suitable assumptions on , 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 functions. Our methods rely on asymptotic expansions for the eigenfunctions and the Harish-Chandra function that we prove under very weak hypotheses.
@article{ASNSP_2009_5_8_2_211_0, 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}, pages = {211--265}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 8}, number = {2}, year = {2009}, mrnumber = {2548246}, zbl = {1171.43005}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2009_5_8_2_211_0/} }
TY - JOUR AU - Brandolini, Luca AU - Gigante, Giacomo TI - Equiconvergence theorems for Chébli-Trimèche hypergroups JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2009 SP - 211 EP - 265 VL - 8 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2009_5_8_2_211_0/ LA - en ID - ASNSP_2009_5_8_2_211_0 ER -
%0 Journal Article %A Brandolini, Luca %A Gigante, Giacomo %T Equiconvergence theorems for Chébli-Trimèche hypergroups %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2009 %P 211-265 %V 8 %N 2 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2009_5_8_2_211_0/ %G en %F ASNSP_2009_5_8_2_211_0
Brandolini, Luca; Gigante, Giacomo. Equiconvergence theorems for Chébli-Trimèche hypergroups. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 8 (2009) no. 2, pp. 211-265. http://www.numdam.org/item/ASNSP_2009_5_8_2_211_0/
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