Linear Ordinary Differential Operators of the Second Order (Classic Reprint) - Hardcover

Ralph S. Phillips

9780267869558: Linear Ordinary Differential Operators of the Second Order (Classic Reprint)

Hardcover

ISBN 10: 026786955X ISBN 13: 9780267869558

Publisher: Forgotten Books, 2020

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Excerpt from Linear Ordinary Differential Operators of the Second Order

A precise meaning will be assigned to the operator (l) in section two for the case when q(x) is real valued, and this will later (section four) be extended to complex q(x). For real q(x) two situations arise depending on the function q(x). In the limit point case there is only one possible interpretation for L and that is independent of a/b L is self-adjoint with a real spectrum. In the limit circle case, L has a pure point Spectrum which lies in the upper half-plane for Im [cl/b] 0 and in the lower half-plane for Im [cc/b] 0. We show by example that in this case the spectrum need not be confined to a strip parallel to the real axis.

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