Index a.e., see also almost everywhere absolue value of an operator, 138 absolute convergence, 20 absolutely continuous function, 95 measure, 331 spectrum, 119 accumulation point, 4 adjoint operator, 54, 67 algebra, 295 almost everywhere, 302 angular momentum operator, 210 B.L.T. theorem, 28 Baire category theorem, 38 ball closed, 6 open, 4 Banach algebra, 29 Banach space, 14 Banach–Steinhaus theorem, 39 base, 5 basis, 17 orthonormal, 47 spectral, 106 Bessel function, 204 modified, 202 spherical, 267 Bessel inequality, 45 bijective, 8 Bolzano–Weierstraß theorem, 12 Borel function, 308 measure, 298 regular, 298 set, 296 σ-algebra, 296 transform, 107, 112 boundary condition Dirichlet, 224 Neumann, 224 periodic, 224 boundary point, 4 bounded operator, 27 sesquilinear form, 26 set, 11 C-real, 93 canonical form of compact operators, 161 Cantor function, 338 measure, 339 set, 302 Cauchy sequence, 7 Cauchy–Schwarz–Bunjakowski inequality, 22 Cayley transform, 91 Ces` aro average, 150 characteristic function, 312 Chebyshev inequality, 339 closable form, 80 operator, 72 closed 353

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