A new cohomology for the Morse theory of strongly indefinite functionals on Hilbert spaces
نویسندگان
چکیده
منابع مشابه
A New Cohomology for the Morse Theory of Strongly Indefinite Functionals on Hilbert Spaces
Take a C function f :M → R on a complete Hilbert manifold which satisfies the Palais–Smale condition. Assume that it is a Morse function, meaning that the second order differential df(x) is non-degenerate at every critical point x. Recall that the Morse index m(x, f) of a critical point x is the dimension of the maximal subspace on which df(x) is negative definite. Then the basic result of Mors...
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Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition fo...
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ژورنال
عنوان ژورنال: Topological Methods in Nonlinear Analysis
سال: 1997
ISSN: 1230-3429
DOI: 10.12775/tmna.1997.017