Properties of kernels of integral equations whose iterates satisfy linear relations Langenhop, Carl
dc.contributor.department Mathematics 2018-08-23T07:31:42.000 2020-06-30T07:24:36Z 2020-06-30T07:24:36Z Thu Jan 01 00:00:00 UTC 1948 1948
dc.description.abstract <p>The principle result obtained in this thesis is the theorem that if the iterated kernels of an integral equation satisfy a linear relation a1K1x,y +a2K2x,y +&cdots;+aKnx,y ≡0,a1≠0, then the kernel K(x,y) must be of the special form i=1N ui(x)vi(y). Using this result it is shown that only such kernels can have a Fredholm determinant D(lambda) and Fredholm first minor D(x,y; lambda) being polynomials in lambda of the same degree. Also in the particular case of a continuous symmetric kernel it is shown that if either D(lambda) or Dx,y;lambda) are polynomials in lambda that then K(x,y) must be of the specia1 form given above;Further properties of idempotent kernels, i.e. ones for which K2x,y≡ K1x,y, are deduced. The connection between such kernels and an idempotent Markoff process is pointed out thus indicating a possible application of the theory of this thesis to certain problems in probability. An alternate proof, of a known result concerning such Markoff processes is given;The results of the thesis are generally derived under the assumption of measurability and boundedness of the kernel K(x,y). Also integration is in the sense of Lebesgue.</p>
dc.format.mimetype application/pdf
dc.identifier archive/
dc.identifier.articleid 13896
dc.identifier.contextkey 6866457
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/12897
dc.language.iso en
dc.source.bitstream archive/|||Fri Jan 14 19:32:26 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.keywords Integral equations
dc.title Properties of kernels of integral equations whose iterates satisfy linear relations
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48 dissertation Doctor of Philosophy
Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
1.92 MB
Adobe Portable Document Format