Index absolute value, 1 absolutely continuous spectrum, 105, 123 Aizenman-Molchanov theory, 113, 133 algebraic multiplicity, 34 Anderson model, 131 antisymmetric tensor product, 6-8 Arazy's theorem, 130 Aronszajn-Krein formula, 91, 105 Auerbach basis, 82 Banach space, 81 Bargmann bound, 62 Berezin inequality, 71 Birman's theorem, 57 Birman-Schwinger bound, 62 Birman-Schwinger kernel, 129 Birman-Schwinger principle, 61 Birman-Solomjak, 38 Borel transform, 86-90 Borg's theorem, 132 Borg-Marchenko theorem, 124 Born expansion, 49 boundary condition dependence, 106 boundary condition variation, 100 Brislawn's theorem, 128 Calderon norm, 9 Calkin property, 18 Calkin space, 18 canonical expansion, 3 Cantor measure, 111 Clarkson-McCarthy inequalities, 14-16 CLR bound, 62 compact operator, 1 completeness, 54 concave trace function, 134 convex hull, 4 convex trace function, 134 Cwikel's theorem, 41 cyclicity, 131 de la Vallee-Poussin theorem, 89, 131 det, 7 determinant, 7, 33 Dirichlet boundary condition, 100 Dirichlet eigenvalue, 117 dominated convergence theorem, 25 doubly substochastic, 5, 9 dss, 5 duality, 31 duality theory, 10 Fatou's lemma, 19 Feynman-Kac formula, 119 finite rank, 1 finitely analytic, 45 fractional moments, 113 Frechet derivative, 45 Fredholm formula, 36, 48 Fredholm minor, 46 Fredholm theory, 45-52 Friedrichs model, 110 Furstenberg's theorem, 108 Gel'fand-Levitan theory, 124 Golden-Thompson inequality, 67, 68 Green's function, 113 Grossman-Wu factorization, 51 Griimm's convergence theorem, 27 Hadamard factorization, 32 Hadamard product formula, 34 Hadamard's inequality, 72 harmonic oscillator, 120 Hausdorff-Young inequality, 40 Hilbert's method, 50 Holder's inequality, 21, 37 Horn's inequality, 7 ideal, 2 infinite coupling, 97-100 integral formula, 92-93 integral kernel, 23 interpolation, 21 Jacobi matrix, 129 Javrjan's theorem, 95

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