REDUCING SCHEMES ON BANACH MANIFOLDS

摘要

Let M be a smooth Banach manifold embedded (as a smooth submanifold) into an affine Banach space E (see [57, 95]) and V be a smooth functional on M smoothly extended to E (the extension is denoted by the same symbol V). Let F and H be Banach and Hilbert spaces, respectively, such that the embeddings E is contained in F is contained in H are continuous and T(E) is dense in H.