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June 1st, 2012, 12:30 PM   #1
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Lower bound of an eigenvalue

For a given real number c>0 define functions }, as an eigenfunctions of the Sturm-Liouville operators L_c defined

( in fact, is called the prolate spheroidal wave function).

Consider a compact integral operator

It is known that are the eigenfunctions of the operator . So,

where are eigenvalues of
(Note, it is known that .)

I would like to find a lower bound for

Any references and ideas will be very helpful.

Thank you.
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June 13th, 2012, 08:35 PM   #2
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Re: Lower bound of an eigenvalue

Ritz or Galerkin method?
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