Research announcement on gaierkirfs method for a class of integra equations of the first kind

Hsiaot, George C.; Wendlandt, Wolfgang

doi:10.1080/00036817708839150

Cited by 4 publications

(1 citation statement)

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“…Furthermore, it is readily appreciated that in more general problems the eigenvalue spectrum of the operators involved is likely to exert a far greater influence on the required analysis than it did in the problems considered in [2]. Recent developments in the theory and application of integral equations of the first kind [3], [5], [4] have made the approach towards the solution of boundary value problems by means of such equations a more attractive proposition. Consequently it should be possible to obtain somewhat similar results to those obtained in [2] provided there exists enough detailed information on the interaction of the various associated spectra.…”

Section: A Symmetric Operator L: H -» H (M: H -» H) Will Be Called a mentioning

confidence: 99%

On the Commutative Properties of Boundary Integral Operators

Roach¹

1979

Proceedings of the American Mathematical Society

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Abstract. A discussion of the interior Dirichlet and Neumann problems of classical potential theory can be given in terms of the symmeterisers of certain related integral operators. Recent developments in the theory and application of integral equations of the first kind have made this approach towards the solution of boundary value problems a more attractive proposition. However for problems more general than those arising in potential theory a greater knowledge of associated spectral properties is required together with a realisation that much of the symmetry occurring in potential problems will be lost and that attention must be directed instead towards commutativity relations. This is demonstrated by considering boundary value problems associated with the Helmholtz equation.

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