Article | REF: AF567 V1

The spectral theory and its applications. Generalities and compact operators

Author: Marc LENOIR

Publication date: April 10, 2010

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5. Elliptic operators

5.1 The abstract point of view

The various problems to which we will apply the preceding theory are presented in the following abstract form: given two Hilbert spaces V and H we assume given a compact application γ : V → H, a coercive sesquilinear form a on V and a continuous antilinear form q on V, we then seek to solve in V the following variational problem [AF 190] ,

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Elliptic operators