## Analysis of operatorsBESTSELLER of the XXth Century in Mathematical Physics voted on by participants of the XIIIth International Congress on Mathematical Physics This revision will make this book mroe attractive as a textbook in functional analysis. Further refinement of coverage of physical topics will also reinforce its well-established use as a course book in mathemtical physics. |

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absolutely continuous algebraic analytic continuation analytic family analytic function argument asymptotic series atom Banach space boundary conditions bounded operator coefficients compute conclude converges Corollary decomposition defined det(l differential equations dilation analytic Dirichlet discrete spectrum discussed eigenfunctions eigenvalue eigenvalue of H0 eigenvector essential spectrum Example family of type finite rank follows formula given ground state energy Hamiltonian Hilbert space hypothesis implies inequality integral kernel Lemma Let H Math matrix method min-max principle Moreover multiplicity N-body negative Neumann nondegenerate norm Notes to Section obeys orthonormal perturbation series perturbation theory Phys positive definite positive eigenvalues positivity preserving potentials Problem proof of Theorem quadratic form quantum Rayleigh-Schrodinger series result Schrodinger operators self-adjoint operator semigroup Simon singular smooth spectral projection strictly positive strong asymptotic subset subspace Suppose Theorem XII trace class unitary vectors virial theorem