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Elements of functional analysis
Differentiation in Banach spaces
6 other sections not shown
Analysis arbitrary assume ball Banach space bilinear form bounded Cauchy sequence chain rule class C1 class Ck components conclude consider contravariant Corollary corresponding covariant derivative curvature deduce defined Definition denote diffeomorphism differentiable in xq differential equation eigenvalues embedding Exercises exists finite Gaussian coordinate system geodesic hence Hilbert space hypersurface induced metric induction inequality initial value problem integral curve isomorphism Lemma Let f Let H Let M,g linear mapping Lorentzian Lp(E,Rn measure space metric space Moreover normed space notation null set open interval open set operator orthogonal outer measure partial derivatives projector Proposition Q C E Radon measure Remark representation resp respect result Riemannian satisfies scalar product semi-Riemannian manifold solution spacelike subspace suppose symbols symmetric tensor field TP(M uniformly uniquely valid variation vector field vector space yields