Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-06-01T20:54:18.767Z Has data issue: false hasContentIssue false
  • English
  • Français

On a method for constructing Bergman kernels

Part of: Representations of solutions Elliptic equations and systems

Published online by Cambridge University Press:  09 April 2009

A. Azzam  and
E. Kreyszig
A. Azzam
Affiliation:
Department of Mathematics University of WindsorWindsor, Ontario N9B 3P4, Canada
E. Kreyszig
Affiliation:
Department of Mathematics University of WindsorWindsor, Ontario N9B 3P4, Canada
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.

We establish a method of constructing kernels of Bergman operators for second-order linear partial differential equations in two independent variables, and use the method for obtaining a new class of Bergman kernels, which we call modified class E kernels since they include certain class E kernals. They also include other kernels which are suitable for global representations of solutions (whereas Bergman operators generally yield only local representations).

MSC classification

Secondary: 35J15: Second-order elliptic equations 35C15: Integral representations of solutions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 4 , June 1980 , pp. 454 - 461
Copyright
Copyright © Australian Mathematical Society 1980

References

Bergman, S. (1969), Integral operators in the theory of linear partial differential equations (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 23, 2nd revised printing, Springer-Verlag, Berlin).Google Scholar
Florian, H. (1962), Normale Integraloperatoren (Habilitationsschrift, Technische Hochschule, Graz). (For an extract, see the next reference.)Google Scholar
Florian, H. (1965), ‘Normale Integraloperatoren’, Monatsh. Math. 69, 18–29.CrossRefGoogle Scholar
Geddes, R. L. and Mackie, A. G. (1977), ‘Riemann functions for self-adjoint equations’, Applicable Anal. 7, 43–47.Google Scholar
Kracht, M. and Schröder, G. (1973), ‘Bergmansche Polynom-Erzeugende erster Art’, Manuscripta Math. 9, 333–355.Google Scholar
Kreyszig, E. (1955), ‘On a class of partial differential equations’, J. Rat. Mech. Analysis 4, 907–923.Google Scholar
Kreyszig, E. (1956), ‘On certain partial differential equations and their singularities’, J. Rat. Mech. Analysis 5, 805–820.Google Scholar
Kreyszig, E. (1973), Gewöhnliche Differentialgleichungen für Erzeugende gewisser Bergman-Operatoren’, J. Reine Angew. Math. 262/263, 74–81.Google Scholar
Meister, V. E., Weck, N. and Wendland, W. L. (1976), Function theoretic methods for partial differential equations (Lecture Notes in Mathematics 561, Springer-Verlag, Berlin).Google Scholar
Watson, G. N. (1966), A treatise on the theory of Bessel functions, 2nd ed. (Cambridge University Press, Cambridge).Google Scholar
Wood, D. H. (1976), ‘Simple Riemann functions’, Bull. Amer. Math. Soc. 82, 737–739.Google Scholar