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Hilbert Space BackgroundSmall Eigen Values
The Fourier Transform Theorem
13 other sections not shown
argument assume Asymptotic Formula bounded operator bounded self-adjoint operator bounded star-shaped subset characteristic function closed linear operator closure complex measurable functions contains a subsequence Corollary define a mapping defined on H denote dense dim E(X dominated convergence theorem Eigen Value Problem equicontinuous family of functions finite positive measure fixed Fourier series Fourier transform given H and H Hilbert space defined homogeneous of degree implies inner product lattice group Lemma 4a Lemma 7b locally star-shaped lowest eigen values multiplicities non-negative Note operators on H perturbation theory point spectrum positive integer positive number positive self-adjoint operator projection on H Proof proved real function real numbers repeated according result satisfy assumptions self-adjoint transformation sesquilinear form space of complex spectral resolution strong limit sufficiently large summands Theorem 3c Theorem 4b Toeplitz operators uniform boundedness principle uniformly bounded values of T*(t verify z)e dz zeros of lower