Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-12-01T02:24:24.634Z Has data issue: false hasContentIssue false
  • English
  • Français

Properties and applications of a certain operator associated with the Kontorovich-Lebedev transform†

Published online by Cambridge University Press:  18 May 2009

Ari Ben-Menahem
Ari Ben-Menahem
Affiliation:
Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel
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 integral

arises in problems of scalar wave propagation in welded elastic wedges. In (1.1), Kim(β1r) is the modified Bessel function of the second kind and m, τ are real. It is shown that Q(τ, m) is a generalized function that includes a complex shift operator. We shall investigate the properties of this operator and establish a new integral transform based on the kernel Q(τ, m).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 16 , Issue 2 , September 1975 , pp. 109 - 122
Copyright
Copyright © Glasgow Mathematical Journal Trust 1975

References

REFERENCES

1.Erdèlyi, A., editor, Tables of integral transforms, Vol. 1 (McGraw-Hill, New York, 1954).Google Scholar
2.Gradshtein, I. S. and Ryshik, I. M., Tables of integrals, series and products (Academic Press, New York, 1965).Google Scholar
3.Magnus, W., Oberhettinger, F. and Soni, R. P., Formulas and theorems for the special functions of Mathematical Physics (Springer-Verlag, Berlin, 1966).CrossRefGoogle Scholar
4.Oberhettinger, F. and Higgins, T. P., Tables of Lebedev, Mehler, and generalized Mehler transforms (Boeing scientific research laboratories Dl–82–0136, 10 1961).CrossRefGoogle Scholar
5.Sneddon, I. N., The use of integral transforms (McGraw-Hill, New York, 1972).Google Scholar
6.Szegö, G., Orthogonal polynomials (Amer. Math. Soc. Providence, R.I., 1959).Google Scholar
7.Titchmarsh, E. C., Some integrals involving Bessel functions, J. London Math. Soc. 2 (1927), 97.CrossRefGoogle Scholar
8.Watson, G. N., A treatise on the theory of Bessel functions (Cambridge, 1966).Google Scholar
9.Whittaker, E. T. and Watson, G. N., A course of modern analysis (Cambridge, 1962).Google Scholar