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An example of an orthogonal transformation of Hilbert sequence space

Published online by Cambridge University Press:  09 April 2009

R. C. T. Smith
R. C. T. Smith
Affiliation:
Mathematics Department The University of New England Armidale
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We use the equivalence of the sequence space 12 and the function space L2 to obtain an orthogonal transformation related to two series inversion formulae due, respectively, to Titchmarsh [1, 2] and to Linfoot and Shepherd [3].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 3 , May 1972 , pp. 357 - 361
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Titchmarsh, E. C., ‘Reciprocal formulae involving series and integrals’, Math. Zeits. 25 (1926), 321–347.CrossRefGoogle Scholar
[2]Titchmarsh, E. C., ‘A series inversion formula’, Proc. London Math. Soc. (2), 26 (1927), 1–11.CrossRefGoogle Scholar
[3]Linfoot, E. H. and Shepherd, W. M., ‘On a set of linear equations (II)’, Quarterly J. Math. (Oxford) 10 (1939), 84–98.Google Scholar
[4]Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G., Tables of Integral Transforms, vol. 2 (McGraw-Hill, New York, 1954).Google Scholar