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Introduction 1 The first elgen value problem
The second elgen value problem
Hllbert Space BackgroundSmall Elgen Values 1 A perturbation problem
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Algebraic argument assertion assume Asymptotic Formula bounded operator bounded self-adjoint operators Chapter characteristic function closure contains a subsequence Corollary 7c defined on H denote dim E(X dominated convergence theorem Edited equicontinuous exists a bounded family of functions finite positive measure follows Fourier series Fourier transform given goes to infinity H and H Hilbert space homogeneous of degree implies inequality inner product large eigen value Lebesgue measure Lemma 3a Lemma 7b Let X(t locally star-shaped mapping measurable functions negative eigen values non-decreasing non-negative operators on H pages 1974 Vol perturbation theory point spectrum positive eigen values Proceedings 1974 projection on H Proof real function real numbers repeated according result satisfy assumptions sesquilinear form SF(t space of complex spectral resolution strong limit sufficiently large summand of H Theorem 3c Toeplitz operators uniform boundedness principle uniformly bounded values of T*(t W(y_ z)e dz