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February 18th, 2013, 07:15 PM   #1
bvh
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if the function sutisfies conditions

For a given real number , denote by are the eigenfunctions of the Sturm-Liouville operators
defined on .

It happened tha the functions are also the eigenfunctions of the compact integral operator defined on by .

Also, are normalized as following
and , where are the infinite sequence of the eigenvalues of , arranged in the non-increasing order and such that .

My question is the following:

If these functions sutisfies the following conditions:

Let . Fix . Can one define A so that and .
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February 18th, 2013, 07:15 PM   #2
bvh
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Re: if the function sutisfies conditions

Quote:
Originally Posted by bvh
For a given real number , denote by are the eigenfunctions of the Sturm-Liouville operators
defined on .

It happened tha the functions are also the eigenfunctions of the compact integral operator defined on by .

Also, are normalized as following
and , where are the infinite sequence of the eigenvalues of , arranged in the non-increasing order and such that .

My question is the following:

If these functions sutisfies the following conditions:

Let . Fix . Can one define A so that and ?

Thank you.
bvh is offline  
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