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On integral transformations with G-function kernels

  • P. G. Rooney (a1)

Synopsis

Integral transformations T of the formal form

where G is a Meijer-G function are studied on the spaces ℐμ,r of functions f such that

Results are obtained on the boundedness, representation and range of the transformations, and on when they have an inverse of the same formal form.

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References

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1Doetsch, G.. Handbuch der Laplace Transformation I (Basel: Birkhauser. 1950)
2Erdélyi, A. et al. Higher transcendental functions I (New York: McGraw-Hill, 1453).
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4Halmos, P. R., A Hilbert space problem book (New York: Van Nostrand, 1967;.
5Kober, H.. Eine Verallgemeinerung der Transformation von Fourier-Typ. Quart. J. Math. Oxford 8 (1937), 172185.
6Luke, Y. L.. The special functions and their approximation (New York: Academic Press, 1969).
7Rooney, P. G.. On the ranges of certain fractional integrals. Canad. J. Math. 24 (1972), 11981216.
8Rooney, P. G.. A technique for studying the boundedness and extendability of certain types of operators. Canad. J. Math. 25 (1973), 10901102.
9Rooney, P. G.. On the extended Hankel transformation. Canad. Math. Bull. 23 (1980), 321325.
10Rooney, P. G.. On the Yv and ℍv transformations. Canad. J. Math. 32 (1980). 10211044.
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12Titchmarsh, E. C.. The theory of Fourier integrals (Oxford: Clarendon, 1937).

On integral transformations with G-function kernels

  • P. G. Rooney (a1)

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