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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