On an Integro-Differential Operator of the Cauchy Type

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Aug 1956Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 7, page 616 (issn: 0002-9939,

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Authors: Elliot, Joanne;

doi: 10.2307/2033360

On an Integro-Differential Operator of the Cauchy Type

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Abstract

the boundary conditions for (1.1) go over into boundary conditions for (1.4). An equation essentially equivalent to (1.3) was derived by Kac in [4] and treated by Kac and Pollard in [5]. Boundary conditions and construction of solutions to (1.1) were considered in [2]. Equation (1.3) with boundary conditions u( -a, t) =u(a, t) =0 is well-known in airfoil theory as a special case of the Prandtl equation, cf. [6]. For X>0, the resolvent equation (1.3) can be solved by reducing it to an integral equation of the Fredholm type, cf. [2] and [6],

Keywords

integral equations, integral transforms

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