Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-09T12:12:06.529Z Has data issue: false hasContentIssue false
  • English
  • Français

Finitely-generated solutions of certain integral equations

Published online by Cambridge University Press:  20 January 2009

D. Porter  and
D. S. G. Stirling
D. Porter
Affiliation:
Mathematics DepartmentThe UniversityPO Box 220Reading RG6 2AX
D. S. G. Stirling
Affiliation:
Mathematics DepartmentThe UniversityPO Box 220Reading RG6 2AX
Rights & Permissions [Opens in a new window]

Abstract

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.

Recent work has shown that the solutions of the second-kind integral equation arising from a difference kernel can be expressed in terms of two particular solutions of the equation. This paper establishes analogous results for a wider class of integral operators, which includes the special case of those arising from difference kernels, where the solution of the general case is generated by a finite number of particular cases. The generalisation is achieved by reducing the problem to one of finite rank. Certain non-compact operators, including those arising from Cauchy singular kernels, are amenable to this approach.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 2 , June 1994 , pp. 325 - 345
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

REFERENCES

1.Gohberg, I. C. and Feldman, I. A., Convolution equations and projection methods for their solution, Transl. Math. Monographs 41 (1974).Google Scholar
2.Mullikin, T. W. and Victory, D., N-Group neutron transport theory: a critical problem in slab geometry, J. Math. Anal. Appl. 58 (1977), 605–630.CrossRefGoogle Scholar
3.Peters, A. S., Abel's equation and the Cauchy integral equation of the second kind, Comm. Pure Appl. Math. 21 (1968), 51–65.CrossRefGoogle Scholar
4.Porter, D., The solution of integral equations -with difference kernels, J. Integral Equations Appl. 3 (1991), 429–454.CrossRefGoogle Scholar
5.Porter, D. and Stirling, D. S. G., Integral Equations (Cambridge University Press, 1990).CrossRefGoogle Scholar
6.Sakhnovich, L. A., Equations with a difference kernel on a finite interval, Russian Math. Surveys 35 (1980), 81–152.CrossRefGoogle Scholar