Hostname: page-component-f554764f5-wjqwx Total loading time: 0 Render date: 2025-04-22T01:00:16.794Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Inversion of the Gauss Transformation

Published online by Cambridge University Press:  20 November 2018

P. G. Rooney
P. G. Rooney*
Affiliation:
University of Toronto
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The inversion theory of the Gauss transformation has been the subject of recent work by several authors. If the transformation is defined by

1.1,

then operational methods indicate that

,

under a suitable definition of the differential operator.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 459 - 464
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Doetsch, G., Handbuch der Laplace-Transformation (Basel, 1950).Google Scholar
2. Eddington, A. S., On a formula for correcting statistics for a known probable error of observation, Monthly Notices Roy. Astron. Soc, 78 (1914), 359–360.Google Scholar
3. Erdélyi, A., et al., Higher Transcendental Functions, vol. 2 (New York, 1953).Google Scholar
4. Erdélyi, A., Higher Transcendental Functions, vol. 3 (New York, 1953).Google Scholar
5. Hirschmann, I. I. and Widder, D. V., The Convolution Transform (Princeton, 1955).Google Scholar
6. Pollard, H., Integral transforms, Duke Math. J., 13 (1946), 307–330.Google Scholar
7. Widder, D. V., The Laplace Transform (Princeton, 1941).Google Scholar
8. Widder, D. V., Necessary and sufficient conditions for the representation of a function by a Weierstrass transform, Trans. Amer. Math. Soc, 71 (1951), 430–439.Google Scholar