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| Stakgold I. — Boundary value problems of mathematical physics |
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| Предметный указатель |
Perpendicular see "Orthogonal"
Poisson summation formula 46 47 50
Polar identity 164
Pole of fundamental solution 62
Polynomials, approximation by see "Weierstrass approximation theorem"
Positive definite, operator see "Positive operator"
Positive definite, quadratic form 112
Positive operator 165 224
Projection 121 149
Projection operator 149
Projection theorem 129
Pseudofunction 48—50
Quadratic form 112
Range of function 93 95
Range of transformation 95
Rank of matrix 79
Rank of transformation on Euclidean space 153
Rayleigh quotient 227
Rayleigh — Ritz procedure for eigenvalues 228
Rayleigh — Ritz procedure for eigenvalues for inhomogeneous equation 245 248
Real operator 225
regular boundary value problem 269
Regular distribution 33
Regular point of differential equation 269 297
Regular transformation on Euclidean space 151
Regular transformation on Hilbert space 166
Resolution of the identity 161
Resonance 82—83
Riemann — Lebesgue lemma 126 185
Riesz representation theorem 136
Riesz — Fischer theorem 122
Ritz — Rayleigh see "Rayleigh — Ritz"
Schroedinger equation 322
Schwarz constants 232
Schwarz inequality 107 109 111 117
Schwarz iteration 231
Schwarz quotients 232
Secular equation 156
Self-adjoint boundary value problem 71
Self-adjoint operators see also "Symmetry"
Self-adjoint operators of differential type 74 219—220
Self-adjoint operators of integral type 212
Self-adjoint operators on Euclidean space 152
Self-adjoint operators on Hilbert space 172
Self-adjoint operators, alternative theorem for 172
Self-adjoint operators, formally 70
Self-adjoint system 71
Separable kernel 192 198 242
Sets of measure zero 105
Sets, bounded 184
Sets, closed 114
Sets, closure of 114
Sets, compact 114 164 184
Sets, dense 114
Sets, exterior of 116
Sets, spanning 119
Shift operator 169
Shift operator, modified 169
Simple eigenvalue 213
singular boundary value problem 269 283—322
Singular boundary value problem in limit-circle case 297 301
Singular boundary value problem in limit-point case 297 301
Singular distribution 33
Singular point of differential equation 59 297
Singular transformation on Euclidean space 151
Singular transformation on Hilbert space 167
Spaces of n-tuples 98 103
Spaces of square integrable functions 111
Spaces of test functions 29
Spaces, Banach 106
Spaces, complex Euclidean 110
Spaces, Hilbert 110 116—190
Spaces, inner product 107
Spaces, linear 96—190
Spaces, metric 99—105
Spaces, real Euclidean 110
Spaces, separable 116
Spaces, vector 96—190
Spanning set 119 128
| Spectral resolution 161
Spectral theorem 160
Spectral theory of second order differential operators 259—322
Spectrum of Hilbert — Schmidt operators 212—220
Spectrum of self-adjoint operator 184
Spectrum of transformation on Hilbert space 180—184
Spectrum, continuous 181
Spectrum, point 181
Spectrum, residual 181
Step response 78
Stirling's formula 27
Successive approximations see "Neumann series"
Superposition principle 4 78
Symbolic function 34 see
Symmetry of differential operator 75—76
Symmetry of Green's function 71
Symmetry of kernel 212
Symmetry of transformation on Euclidean space 152 159
Symmetry of transformation on Hilbert space 172
system see also "Boundary value problem"
System, adjoint 69—71
System, self-adjoint 71
Test functions 28—30
Test functions, complex-valued 34
Test functions, convergence for 30
Test functions, space of 29
Transformations 94 139—190 191—258
Transformations on Euclidean space 146—165
Transformations on Hilbert space 139—146 165—190
Transformations, adjoint 152 170
Transformations, bounded 140
Transformations, closed 142 168
Transformations, commuting 139
Transformations, completely continuous 185
Transformations, continuous 140
Transformations, domain of 139
Transformations, eigenvalues of 154
Transformations, eigenvectors of 154
Transformations, extensions of 141
Transformations, indefinite 165
Transformations, integral 144 191—258
Transformations, inverse of 95 140 151 166
Transformations, kernel of 144 192
Transformations, linear 140
Transformations, negative and nonnegative 165
Transformations, null space of 139 143 171
Transformations, nullity of 153
Transformations, one-to-one 139 166
Transformations, positive and nonpositive 165
Transformations, projection 149
Transformations, range of 139 171
Transformations, rank of 153
Transformations, regular 151 166
Transformations, self-adjoint 152
Transformations, singular 151 167
Transformations, symmetric 152 159 172
Transformations, unbounded 145
Translation of distribution 35
Transposed matrix 80
Triangle inequality 100
Uniqueness see "Existence and uniqueness"
Variation iteration 231
Variational principles see "Extremal principles"
Vector spaces 96—99 105—190
Vector spaces, basis for 97—98
Vector spaces, complex 96—97
Vector spaces, dimension of 97
Vector spaces, inner product on 107 109
Vector spaces, normed 104
Vector spaces, real 96
Volterra integral equations 196 209—211
Wave equation 325—326
Weak solutions of differential equations 53
Weierstrass approximation theorem 27 115
Weyl's theorem 297
Wronskians 59—61
Wronskians for Bessel functions 330—331
Wronskians, Abel's formula for 60
Wronskians, Green's functions and 272
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