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Gap Formulae for the Weierstrass Transforms

Published online by Cambridge University Press:  20 November 2018

Z. Ditzian
Z. Ditzian*
Affiliation:
University of Alberta Edmonton
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A gap formula for a transform

(1)

is an operator J on f(x)

(2)

Such operators are known for Laplace transform [1; p.91] and [4; pp. 296–299], Stieltjes transform [4; pp. 351–353], a class of convolution transforms [2] and others. Gap formulae for the Weierstrass transform

(3)

and the Weierstrass-Stieltjes transform

(4)

will be proved in the following two theorems.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 2 , June 1968 , pp. 249 - 254
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Ditzian, Z. and Jakimovski, A., Real inversion and jump formulae for the Laplace transform (Part I), Israel Jour, of Math. 1 (1963) 85-104.Google Scholar
2. Ditzian, Z., A complex jump formula for a class of convolution transforms. Illinois Jour, of Math. (1967) 375-388,Google Scholar
3. Hirschman, I.I. and Widder, D.V., The convolution transform. (Princeton Univ. Press, 1955).Google Scholar
4. Widder, D.V., The Laplace transform. (Princeton Univ. Press, 1946).Google Scholar