356 INDEX OF TERMINOLOGY Gram-Schmidt orthogonalization, 133, 339 greatest integer function, 295 greatest lower bound, 3, 306 greatest lower bound property, 3 group, 326, 340 group of norms, 95 group of units, 87 Haar basis, 258 Haar integral, 231 Haar measure, 194, 227, 240, 246 half-open rectangle, 181, 195, 203 Hamel basis, 319 harmonic series, 27 Hausdorff topological space, 67, 70, 96, 97 heat equation, 238 Heine-Borel theorem, 16, 22, 56, 57, 59, 88 Hessian, 168, 169 Hilbert space, 126, 128, 129, 131, 132, 134, 136, 140, 233, 234, 258, 267 Hilbert space adjoint, 130 older’s inequality, 35, 103, 217, 218, 222 homeomorphic, 77, 248 homeomorphism, 49, 57, 66, 70, 96, 201 homogeneous space, 96–98 homomorphism, 231, 233, 239, 246, 343 homomorphism of topological groups, 98, 99 hyperplane, 333 ideal in a ring, 87 idempotent operator, 129 identity, function, 291, 293 ILC, 288 image, 292 imaginary part, 19 Implicit Function Theorem, 175, 176, 179, 180 inclusion-exclusion principle, 279 independence of axioms, 310 index set, 277 indiscrete topology, 65 infimum, 55, 306 infinite series, 26, 89, 90 infinite set, 298, 302 infinite-dimensional representation, 233, 267 infinite-dimensional vector space, 319 infinitely differentiable function, 248 injective, 292 inner product, 126, 128, 129, 132, 257 inner regular Borel measure, 200 integrable function, 212–215, 220, 230 integral, 208, 209, 212, 213, 215, 251 integral domain, 288 interior, 42, 65, 80, 143, 181 Intermediate Value Theorem, 61, 176 Intermediate Value Theorem for Derivatives, 146 internal law of composition, 288 intersection, 274 intertwining operator, 235 interval, 8, 61 invariant subspace, 233, 235, 237 inverse Fourier transform, 251 Inverse Function Theorem, 175, 176, 178, 179 inverse of a function, 294 invertible matrix, 324 irrational number, 4, 33, 101 irreducible representation, 232, 233, 235, 265, 267, 269 isolated point, 40, 80 isometric, 49, 77 isometric isomorphism, 119 isometrically isomorphic, 258 isometry, 49, 116, 118, 119, 141, 238, 258 isometry group, 120, 121, 123 isomorphic, 248 isomorphism of groups, 343 isomorphism of topological groups, 98, 99 Iwasawa decomposition, 141 Jacobian matrix, 155, 170, 175, 224, 225 Jordan content zero, 189 Jordan domain, 189 kernel, 99, 108, 250 kernel of a homomorphism, 343 kernel of a linear transformation, 321 L’Hˆ opital’s rule, 146, 147 Lagrange multiplier, 170–173 Laplace transform, 238, 255 lattice, 83, 84, 206 lattice operations, 55 lattice point, 1, 80 lattice polygon, 1 lattice polyhedron, 1 least upper bound, 2, 72, 306
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