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Some Remarks on Left-Definite Hamiltonian Systems in the Regular Case

✍ Scribed by Rolf Vonhoff

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
629 KB
Volume
193
Category
Article
ISSN
0025-584X

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✦ Synopsis

It is the aim to confront recent considerations of A. M. KRALL on the left-definite spectral theory of regular Hamiltonian systems with the results of former research in this field. A short survey of the main sources starting with the work of E . HOLDER in 1935 is given. After that the essential features of the left -definite Shermitian theory, as it was developed by SCHAFKE and SCHNEIDER in 1965, are presented for the special case of the problems treated by KRALL, and an application to Sturm -Liouville equations is given. By comparing methods and assumptions of both theories, it is shown that the main result in KRALL'S papers, a theorem on eigenfunction expansions, can be obtained under much weaker conditions. Especially one gets rid of the problem that the restrictions in the work of KRALL even exclude the classical polar case which builds the startingpoint of the leftdefinite theory.

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