Singular Integral Equations
dc.contributor.author | Case, K. M. | en_US |
dc.date.accessioned | 2010-05-06T22:43:52Z | |
dc.date.available | 2010-05-06T22:43:52Z | |
dc.date.issued | 1966-12 | en_US |
dc.identifier.citation | Case, 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.uri | https://hdl.handle.net/2027.42/70799 | |
dc.description.abstract | The 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.extent | 3102 bytes | |
dc.format.extent | 230991 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.publisher | The American Institute of Physics | en_US |
dc.rights | © The American Institute of Physics | en_US |
dc.title | Singular Integral Equations | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Physics, The University of Michigan, Ann Arbor, Michigan | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/70799/2/JMAPAQ-7-12-2121-1.pdf | |
dc.identifier.doi | 10.1063/1.1704897 | en_US |
dc.identifier.source | Journal of Mathematical Physics | en_US |
dc.identifier.citedreference | A. 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.citedreference | Here and throughout this article P is to remind us that principal values are to be used when integrating the kernels. | en_US |
dc.identifier.citedreference | See, 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.citedreference | The 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.citedreference | This is, of course, compatible with the earlier restriction m = 0.m=0. | en_US |
dc.identifier.citedreference | I am indebted to the referee of this paper for informing me that unpublished notes of Peters exist to this effect. | en_US |
dc.owningcollname | Physics, Department of |
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