Bingham, N. H.; Inoue, A. Ratio Mercerian theorems with applications to Hankel and Fourier transforms. (English) Zbl 1030.44005 Proc. Lond. Math. Soc., III. Ser. 79, No. 3, 626-648 (1999). We complete and complement our recent work on Drasin-Shea-Jordan theorems for Fourier and Hankel transforms [cf. N. H. Bingham and A. Inoue, Q. J. Math., Oxf. II. Ser. 48, No. 191, 279-307 (1997; Zbl 0889.42005)]. In improving on the methods of our previous work, we were led to certain ratio Mercerian theorems for general kernels; these yield definitive versions of our earlier results for Fourier and Hankel transforms. Reviewer: Akihiko Inoue (Sapporo) Cited in 1 ReviewCited in 3 Documents MSC: 44A15 Special integral transforms (Legendre, Hilbert, etc.) 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 47B38 Linear operators on function spaces (general) Keywords:Fourier transform; Hankel transform; regular variation; ratio Mercerian theorems Citations:Zbl 0889.42005 PDFBibTeX XMLCite \textit{N. H. Bingham} and \textit{A. Inoue}, Proc. Lond. Math. Soc. (3) 79, No. 3, 626--648 (1999; Zbl 1030.44005) Full Text: DOI