Geodesic
A spectral approach to an integral equation
Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 83-89

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In a recent paper [7], Rooney used a technique involving the Mellin transform to obtain solutions in certain spaces Lμ, ρ of an integral equation which had been studied previously by Šub-Sizonenko [9]. The integral equation in question can be written aswhere I denotes the identity operator and G0.1/2 is given bywith the inversion formula obtained by Rooney taking the formRooney verified that (1.1) and (1.2) formed an inversion pair in Lμ, ρ for 1 ≤ p < ∞ and μ > 0. 
Lamb, W. A spectral approach to an integral equation. Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 83-89. doi: 10.1017/S0017089500005802
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[1] 1.Balakrishnan, A. V., Fractional powers of closed operators and semigroups generated by them, Pacific J. Math. 10 (1960), 419–437. Google Scholar | DOI

[2] 2.Erdélyi, A. et al. , Higher transcendental functions I (McGraw-Hill, 1953). Google Scholar

[3] 3.Hövel, H. W. and Westphal, U., Fractional powers of closed operators, Studia Math. 42 (1972), 177–194. Google Scholar | DOI

[4] 4.Lamb, W., Fractional powers of operators on Fréchet spaces with applications (Strathclyde Univ. Ph.D. Thesis, 1980). Google Scholar

[5] 5.Lamb, W., Fractional powers of operators defined on a Fréchet space, Proc. Edinburgh Math. Soc. (2), (to appear). Google Scholar

[6] 6.Love, E. R., Some inequalities for fractional integrals, Linear spaces and approximation, Proc. Conf., Math. Res. Int. Oberwolfach, 1977, Internat. Ser. Numer. Math., 40 (Birkhauser, 1978). Google Scholar

[7] 7.Rooney, P. G., On an integral equation of Šub-Sizonenko, Glasgow Math. J. 24 (1983), 207–210. Google Scholar | DOI

[8] 8.Rooney, P. G., Multipliers for the Mellin transformation, Canad. Math. Bull. 25 (1982), 257–262. Google Scholar | DOI

[9] 9.Šub-Sizonenko, J. A., Inversion of an integral operator by the method of expansion with respect to orthogonal Watson operators, Siberian Math. J. 20 (1979), 318–321. Google Scholar | DOI

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