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I was reading the Wiki page on the Sturm-Liouville theory. Why are those tenets true? Are there any (not too advanced) reference material?

I have also read that

"There are countably infinite number of eigenvalues which satisfy the self-adjoint problem due to the property of completeness." -- someone's old notes

Firstly, why is the property of completeness true?

Secondly, why is this quoted statement true?

Thanks

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    @HenningMakholm: I was referring to the section under the subtitle [Sturm–Liouville theory](http://en.wikipedia.org/wiki/Sturm_liouville#Sturm.E2.80.93Liouville_theory).2011-09-25
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    @HenningMakholm: I am sorry. I meant the 3 statements: 1) the eigenvalues of the SL problem are real and can be ordered. 2) corresponding to each eigenvalue $λ_n$ is a unique (up to a normalization constant) eigenfunction $y_n(x)$ which has exactly $n-1$ zeros in $(a, b)$ and 3)The normalized eigenfunctions form an orthonormal basis in the Hilbert space. I am also not sure what the $n-1$ zeros refer to.2011-09-25
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    So basically you're asking for a proof of the theorem?2011-09-25
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    @HenningMakholm: Yes please (or a reference), and perhaps a clarification on what the $n-1$ zeros are. Also, an explanation of the quoted statement about completeness... Thanks. :-)2011-09-25
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    The wikipedia article itself gives references. Have you looked at them? If they are not satisfactory to you, please tell us why...2011-09-25
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    @PeteL.Clark: I have looked at them, well the one available online. But they seem aimed at more advanced students -- there are quite a lot of material (regarding the SLT bits) that I am not familiar with. I was hoping for a perhaps simpler explanation?2011-09-25
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    A very nice introductory reference for the topic is "Fourier Series and Orthogonal Functions" by Harry Davis, of Dover publications. I think they have a Kindle edition now. Cheers. Juan Pablo2013-09-06

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