From: schleeha@aol.com (Schleeha)
Newsgroups: sci.math
[1] Proof of Completeness of Sturm-Liouville Solutions?
Date: 22 Dec 1996 21:55:50 GMT
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I have heard it asserted that the solutions to any Sturm-Liouville problem
forms a complete set of orthogonal functions. However, I have not been
successful at finding a proof that the solutions form a complete set,
meaning
that any (well-behaved) arbitrary function on the interval of
orthogonality
can be expressed as a linear combination of the solutions. All references
to
this assertion have included statements like, "The proof is too
complicated
for inclusion in this text...the interested reader can refer to XYZ." I
have
followed all leads, and it turns out that the references "XYZ" do not
contain
the proof either. Any help in this area would be much appreciated.
End of article 173515 (of 173787) -- what next? [npq] sci.math #173666 (18 + 1051 more) (1)+-[1]
From: kochman@harder.ccr-p.ida.org (Fred Kochman) \-[1]
[1] Re: Proof of Completeness of Sturm-Liouville Solutions?
Proofs can be found in many textbooks. Two that come to mind
are the ones by Birkhoff and Rota, and the one by Phillip Hartman.
End of article 173666 (of 173787) -- what next? [npq] sci.math #173708 (17 + 1051 more) (1)+-(1)
From: "N. Shamsundar" \-[1]
[1] Re: Proof of Completeness of Sturm-Liouville Solutions?
For a proof, based on Parseval's equality, see Redheffer's "Differential
Equations", Jones & Bartlett, 1991, p.447. He excuses himself from the
proof of the converse theorem for the reason that it requires the
Lebesgue integral.