Methods of Hilbert Spaces |
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A₁ absolutely convex adjoint algebra arbitrary Banach space basis of neighbourhoods bilinear bornological boundary conditions bounded sets C*-algebra called Chapter closed coefficients commutative compact operator compact set complete continuous functions continuous linear COROLLARY countable defined definition denote dense differential operators Dirichlet domain Ehrling eigenvalues element elliptic operator exists finite-dimensional following THEOREM formula function f Gårding H₁ Hermitian operator Hilbert space holomorphic identity implies inequality integral isometric isomorphism kernel LEMMA linear functional linear map locally convex manifold measure Methods of Hilbert metric space neighbourhood of zero Neumann normed space nuclear obtain open set orthonormal P₁ problem Proof prove representation satisfies scalar product Section self-adjoint extension self-adjoint operator seminorm solution space H spectral theorem spectrum subset subspace Suppose theory topology transformation u₁ u₂ unitary space vanishing vector space weakly whence X₁