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Ratio Mercerian theorems with applications to Hankel and Fourier transforms. (English) Zbl 1030.44005

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.

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)

Citations:

Zbl 0889.42005
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