Ordinary differential operators in Hilbert spaces and Fredholm pairs |
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Authors: | Alberto Abbondandolo Pietro Majer |
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Affiliation: | (1) Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy , IT;(2) Dipartimento di Matematica “L. Tonelli”, Università di Pisa, Via F. Buonarroti 2, 56127 Pisa, Italy , IT |
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Abstract: | Let be a path of bounded operators on a real Hilbert space, hyperbolic at . We study the Fredholm theory of the operator . We relate the Fredholm property of to the stable and unstable linear spaces of the associated system . Several examples are included to point out the differences with respect to the finite dimensional case, in particular concerning the role of the spectral flow. We define a general class of paths A for which many properties typical of the finite dimensional framework still hold. Our motivation is to develop the linear theory which is necessary for the set-up of Morse homology on Hilbert manifolds. Received: 9 March 2001; in final form: 1 March 2002 / Published online: 2 December 2002 |
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