An Application of Spectral Properties of Non-support Operators to a Theorem of S. Karlin

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概要

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• Recently, S. Karlin has shown the existence of infinite eigenvalues for integral operators with extended totally positive kernels or more general kernels [1]. Each of these kernels must satisfy some conditions of differentiability. In the following note, we shall show that, applying the spectral properties of non-support operators obtained by the author [3], the above Karlin's results can be extended to the case of integral operators without differentiability conditions. For example, as one of these kernels, we can take a kernel K (x, s) of Schmidt type on (a, b)×(a, b) which is totally positive, continuous (not necessarily symmetric) and satisfies [numeberical] The author wishes to express her hearty thanks to Prof. S. Karlin for his valuable informations and remarks given her during his stay in Japan.

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著者

• 沢島 侑子

  Department Of Mathematics Faculty Of Science Ochanomizu University

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