Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-04T21:32:06.718Z Has data issue: false hasContentIssue false

A note on Watson transforms

Published online by Cambridge University Press:  24 October 2008

H. S. V. De Snoo
Affiliation:
Mathematisch Instituut, Rijksuniversiteit Groningen, Postbus 800, Groningen, Nederland

Extract

In (6) Plancherel considered linear, bounded transforms which satisfy

where the linear, bounded transform is defined by

Among other things he proved: if W1, W2 and W3 are linear, bounded transforms satisfying (1), then

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bochner, S. and Chandrasekharan, K.Fourier Transforms. Annals of Mathematical Studies 19 (Princeton, 1949).Google Scholar
(2)Goldberg, R.R.Convolutions and general transforms on L D Duke Math. J. 27 (1960), 251259.CrossRefGoogle Scholar
(3)Goldberg, R. R.Watson transforms on groups. Ann. of Math. 71 (1960), 522528.CrossRefGoogle Scholar
(4)Kober, H.Eine Verallgemeinerung der Transformationen vom Fourier-Typ. Quart. J. Math. Oxford 8 (1937), 172185.CrossRefGoogle Scholar
(5)Leibowitz, G. M.On a theorem concerning Watson transforms. J. Math. Anal. Appl. 16 (1966), 308310.CrossRefGoogle Scholar
(6)Plancherel, M.Quelques remarques à propos d'une note de G. H. Hardy: The resultant of two Fourier kernels. Proc. Cambridge Philos. Soc. 33 (1937), 413418.CrossRefGoogle Scholar
(7)Titchmarsh, E. C.Introduction to the theory of Fourier integrals, 2nd ed. (Oxford, 1948).Google Scholar