Separation of Variables and Wiener-Hopf Techniques (Classic Reprint) - Couverture souple

Samuel N. Karp

 
9781330156476: Separation of Variables and Wiener-Hopf Techniques (Classic Reprint)

Synopsis

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Présentation de l'éditeur

The role played by the fT inetion-theoretic Wiener-H opf techniques in the solution of certain integral equations arising from the application of Green stheorem to boundary value problems le well known and has recently been extended. In the present work we discuss and illustrate the relevance and applicability of these techniques when the method of separation of variables in cuiT vilinear coordinates is employed. For the same boundary various appropriate or semi-appropriate coordinate systems may be employed, while on the other hand the Green sfunction integral equation is invariant. There is seen to be a correspondence between the two methods, which are expressions of the duality between Green sfunction and eigenfunction techniques. Various aspects of this correspondence, as well as the effect of change of coordinete systems ere illustrated. The resulting relationships shed some lit on the problem of recognizing the relevancy of Wiener-H opf or more classical techniques to certain integral equations and serves as a guide in the discovery of new problems to which the method (in either guise mentioned above) may be applied. Certain observations with regard to tiniqueness also result.
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