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