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February 18th, 2013, 07:15 PM  #1 
Newbie Joined: Feb 2013 Posts: 16 Thanks: 0  if the function sutisfies conditions
For a given real number , denote by are the eigenfunctions of the SturmLiouville 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 nonincreasing 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 . 
February 18th, 2013, 07:15 PM  #2  
Newbie Joined: Feb 2013 Posts: 16 Thanks: 0  Re: if the function sutisfies conditions Quote:
 

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