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Singular Integral Equations

dc.contributor.authorCase, K. M.en_US
dc.date.accessioned2010-05-06T22:43:52Z
dc.date.available2010-05-06T22:43:52Z
dc.date.issued1966-12en_US
dc.identifier.citationCase, K. M. (1966). "Singular Integral Equations." Journal of Mathematical Physics 7(12): 2121-2124. <http://hdl.handle.net/2027.42/70799>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/70799
dc.description.abstractThe integral equationP∫cK(ζ′,ζ)ζ′−ζφ(ζ′)dζ′=h(ζ)φ(ζ)+f(ζ)is shown to have simple solutions obtained by standard and elementary methods if h and K have appropriate analytic properties.en_US
dc.format.extent3102 bytes
dc.format.extent230991 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleSingular Integral Equationsen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Physics, The University of Michigan, Ann Arbor, Michiganen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/70799/2/JMAPAQ-7-12-2121-1.pdf
dc.identifier.doi10.1063/1.1704897en_US
dc.identifier.sourceJournal of Mathematical Physicsen_US
dc.identifier.citedreferenceA. S. Peters, Commun. Pure Appl. Math. XVIII, 129 (1965). I am indebted to Professor C. L. Dolph for calling my attention to this article.en_US
dc.identifier.citedreferenceHere and throughout this article P is to remind us that principal values are to be used when integrating the kernels.en_US
dc.identifier.citedreferenceSee, for example, N. I. Muskhelishvili, Singular Integral Equations (P. Noordhoff Ltd., Gröningen, The Netherlands 1953). To be precise we mean by “standard” the method described in Chap. 6 of this reference. It is introduced with the words: “This method is the one most frequently used up to the present; it was suggested (in different particular applications) by the founders of the theory of singular equations—Poincaré and Hilbert.” Apparently Peters had a different definition of “standard” method in mind.en_US
dc.identifier.citedreferenceThe fact that an explicit integral representation for such a Y(z) exists is of no importance for the considerations of this article.en_US
dc.identifier.citedreferenceThis is, of course, compatible with the earlier restriction m  =  0.m=0.en_US
dc.identifier.citedreferenceI am indebted to the referee of this paper for informing me that unpublished notes of Peters exist to this effect.en_US
dc.owningcollnamePhysics, Department of


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