Functional Analysis
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Contents
Linear Maps | 8 |
The HahnBanach Theorem | 19 |
Applications of the HahnBanach theorem | 29 |
Copyright | |
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According to theorem adjoint analytic function Banach algebra Banach space belongs boundary bounded linear map Cauchy sequence chapter claim Clearly closed closure commute compact map compact operator complex numbers conclude contains continuous function converges convex deduce defined definition denote dense derivatives differential distribution eigenfunctions eigenvalues eigenvectors Exercise finite follows formula Fourier transform function f harmonic function Hilbert space homomorphism integral operator invariant subspace invertible kernel lemma Math measure multiplicity nonnegative nonzero nullspace one-parameter open set orthogonal orthonormal polynomial positive precompact properties proves pseudoinverse range real numbers resolvent set right side satisfies scalar product self-adjoint operator semigroup solution space H spectral representation spectral resolution spectrum strongly continuous subset Suppose symmetric operator tends to zero Theorem 11 theory topology trace class uniformly unit ball unit disk unitary operators vector wave equation wave operators