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| Egorov Y.V., Shubin M.A. — Partial Differential Equations I (Foundations of the Classical) |
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| Предметный указатель |
Fredholm property of solutions of elliptic boundary-value problems 109
Fredholm, E.I. 98 104 109 131
Friedman, A. 104 171 176 242 244
Friedrichs' inequality 124
Friedrichs, K.O. 127
Front, wave 145
Function(s) Airy 236—237
Function(s) Bessel's of first kind 229
Function(s) Bessel's of imaginary argument 232
Function(s) convolution of 63
Function(s) cylindrical 226
Function(s) cylindrical of second kind 231
Function(s) delta-, delta-shaped family 51
Function(s) delta-Dirac 47
Function(s) eigen- 126
Function(s) eigen- Bloch 218
Function(s) eigen- continuous spectrum 194
Function(s) elliptic cylinder 240
Function(s) generalized (distribution) 47
Function(s) generalized homogeneous 59
Function(s) generalized spherically symmetric 70
Function(s) generalized tempered 49
Function(s) generating for the Hermite polynomials 239
Function(s) generating for the Laguerre polynomials 239
Function(s) generating for the Legendre polynomials 223
Function(s) Green's for a Sturm — Liouville problem 202
Function(s) Green's for the Dirichlet problem 88
Function(s) Hankel of first kind 231
Function(s) Hankel of second kind 231
Function(s) harmonic 83
Function(s) Heaviside 56
Function(s) hypergeometric 241
Function(s) hypergeometric confluent 240
Function(s) Kummer 240—241
Function(s) Legendre, associated 221
Function(s) Macdonald 233
Function(s) Mathieu 240
Function(s) Neumann 231
Function(s) of a surface 64
Function(s) parabolic cylinder 240
Function(s) source for a Sturm — Liouville problem 202
Function(s) source for the Dirichlet problem 88
Function(s) special 220—241
Function(s) support of 48
Function(s) test 48
Galerkin, B.G. 125
Garding's theorem 137
Garding, L. 137 150 178 242—244
Gauss' hypergeometric series 241
Gauss, K.F. 241
Gel'fand, I.M. 47 51 55 58 61 62 65 164 172 220 242
Generalized function (distribution) convolution of 63
Generalized function derivative of 55
Generalized function homogeneous 59
Generalized function regularization of 60
Generalized function spherically symmetric 70
Generalized function support of 53
Generalized function tempered 49
Generalized function tempered, Fourier transform of 65
Generalized solution of a differential equation 123
Generating function for Hermite polynomials 239
Generating function for Laguerre polynomials 239
Generating function for Legendre polynomials 223
Geometric-optical ray 191
Gindikin, S.G. 25
Glazman, I.M. 216 243 244
Gokhberg, I.Ts. 187 244
Gordon, W. 18
Green's formula 84
Green's formula second 84
Green's function for a Sturm — Liouville problem 202
Green's function for the Dirichlet problem 88
Green, G. 70 84 88—90 92 161 202 203
Hadamard's example 21
Hadamard's Theorem 178
Hadamard, J. 21 24 138 177—179
Hamilton — Jacobi equation 45
Hamilton, W.R. 45 46 157
Hamiltonian system 191
Hankel functions of first kind 231
Hankel functions of second kind 231
Hankel transform 234
Hankel, H. 188 231 232 234
Harmonic functions 83
Harmonic spherical 220
Harnack's inequality 91
Harnack's theorem 88
Harnack, A. 87 88 91
Hartman, P. 41 150 231 244
Heat equation 10 37
Heat operator, fundamental solution for 72
Heat potential 76
Heaviside function 56
Heaviside, O. 56 66 71 155
Helmholtz' equation 15
Helmholtz, G. 15 17 184 233
Herglotz — Petrovskij formulas 144
Herglotz, G. 144 145 150
Hermite polynomials 239
Hermite, Ch. 18 239
Hilbert transform 65
Hilbert, D. 65 104 113 126 181 202 204 243 244
Hill operator 218
Hill, G.W. 218
Hille — Yosida theorem 181
Hille, E. 181
Hoelder spaces 99
Hoelder spaces estimates in 167
Hoelder, O. 110 120 131 162 173
Hoermander, L. 20 24 33 47 51 53 55 57—59 62 65 66 68 69 73 77 79 83 105 122 170 191 236 238 242 245
Holmgren's theorem 35—36
Holmgren, A. 25 35
Hooke, R. 9 10
Hugoniot, H. 135
Huyghens' principle 145
Huyghens, Ch. 145
Hyperbolic equation at a point 38
Hyperbolic equation discontinuous solution of 153—157
Hyperbolic equation in a region 38
Hyperbolic equation in the direction of a vector 43
Hyperbolic operator 38
Hyperbolic operator at a point 38
Hyperbolic operator in a region 38
Hyperbolic operator in the direction of a vector 43
Hyperbolic polynomial 26
Hyperbolic symmetric system 44
Hypergeometric equation 241
Hypergeometric functions 241
Hypergeometric functions confluent 240
Hypergeometric series of Gauss 241
Hypoelliptic operator 78
Il'in, A.M. 165 167 168 171 173 176 242 245
Il'in, V.P. 113 245
Imbedding theorems 119—122
Index defect 212
Index of a boundary-value problem 110
Index of an operator 110
Index of parabolicity of a system 172
Inductive limit topology 50
Inequalities, energy 159
Inequality Friedrichs' 123
Inequality Harnack's 91
Infinitesimal generator of a semigroup 180
Initial condition 11
Inner capacity 101
Integral Dirichlet 123
Integral estimates 166
Integral singular 65
Interior a priori estimate 87
Interior Dirichlet problem 87
| Jacobi, K.G.J. 45 46
Jahnke, E. 243 245
John, F. 38 113 122 132 134 144 147 177 243 245
Jump theorems for double-layer potential 95
Jump theorems for single-layer potential 95
Kalashnikov, A.S. 132 165 167 168 171 173 177 176 242 245
Kato's theorem 182
Kato, T. 182 188
Kellogg's theorem 104
Kellogg, O.D. 104
Kelvin transform 92
Kelvin, W. 92 93 98
Kernel Dirichlet 51
Kernel Fejer 51
Kernel generalized 68
Kernel of an operator, in the sense of Schwartz 68
Kirchhoff's formulas 142
Kirchhoff, G.R. 142 144
Klein — Gordon — Fock equation 18
Klein, F. 241
Klein, O. 18
Komatsu, H. 245
Korteweg, D.J. 207
Kostyuchenko, A.G. 214 217 144 243 245
Kovalevskaya type 28—29
Kovalevskaya, S.V. 28—33 36
Kreiss' example 178
Kreiss, H.O. 159 245
Krejn, M.G. 187
Krejn, S.G. 183 184 242 245
Kummer function 240—241
Kummer, E.E. 240 241
Lacuna 150 218
Lacuna strong 150
Ladyzhenskaya, O.A. 99 104 113 122 132 134 242 243 245
Laguerre polynomials 239
Laguerre, E.N. 239 240
Landau, L.D. 16 242 245
Landis, E.M. 85 100 246
Landkof, N.S. 85 100 102 208 209 242 245
Laplace transform 133 179
Laplace — Beltrami operator 15
Laplace's equation 14 37 220
Laplace's formulas 226
Laplace, P.S. 14 21 22 24 37 88 99 223
Laplacian 10
Laplacian fundamental solution for 70 83
Laurent, P.A. 82
Lax — Phillips theorem 184
Lax, P. 140 184 199 244 245
Lebesgue, H. 47 54
Legendre functions, associated 221
Legendre polynomials 144
Legendre polynomials of first kind 238
Legendre polynomials of second kind 238
Legendre's equation 225
Legendre, A.M 144 221 223 225 241
Leibniz, G.W. 5 56 71
Lemma, normal derivative 86
Levinson, N. 207 243
Levitan, B.M. 206 220 243 245
Lifshits, E.M. 16 243 245
Light cone 73
Limiting absorption 189
Limiting amplitude 189
Linear differential operator 7
Linear partial differential equation 7
Lions, J.L. 105 113 122 242 243 245
Liouville's theorem 80 91
Liouville, J. 77 80 92 201 202 203 205
Local energy 191
Local operator 69
Lopatinskij, Ya. B. 105
Lorentz, H.A. 18
Losch, F. 243 245
Macdonald function 233
Macdonald, H.M. 233
Magenes, E. 105 113 122 242 243 245
Majorants, method of 28
Manakov, S.B. 207 218
Marchenko, V.A. 209 215 216 243 246
Mathieu E.L. 240
Mathieu functions 240
Mathieu's equation 240
Matrix, scattering 198
Maximal operator 212
Maximum principle 24
Maximum principle for a general elliptic equation 104
Maximum principle for a parabolic equation 164
Maximum Principle for harmonic functions 87
Maximum principle strong 165
Maxwell's equations 15—16
Maxwell, J.C. 15 16 18 158
Maz'ya, V.G. 100 113 243 246
Mean-value theorem for harmonic functions 85
Measure, Radon 54
Mehler 226
Mehler's formulas 226
Method balayage 102
Method Cook's 196
Method descent 142
Method energy 135
Method energy estimates 138
Method Fourier transform 142
Method Fourier's 135 163
Method majorants 28
Method plane wave 145
Method separation of variables 135 163
Mikhailov, V.P. 87 92 113 122 132 242 246
Mikhlin, S. G. 87 94 97 113 122 223 242 243 246
Miller, W. 243 246
Minimal operator 212
Miranda, M. 99 104 113 242 246
mixed boundary-value problem 159—161
Mixed parabolic problem 132
Mizohata's theorem 138
Mizohata, S. 122 134 138 141 178 179 246
Molchanov's theorem 214
Molchanov, A.M. 214 217
Monodromy operator 218
Morawetz, C.S. 192
Multiplier, Floquet 219
Najmark, M.A. 211 214 220 243 246
Nash's theorem 167—168
Nash, J. 167
Neumann condition 14—15
Neumann functions 231
Neumann problem 87
Neumann problem exterior 93
Neumann problem generalized statement of 128
Neumann, K.G. 14 83 87 93 98 110 128 160 189 231
Newton, I. 5 9 96
Newton, R.G. 199 243 246
Newtonian potential 63 94
Nikol'skij, S.M. 113 243 246
Nirenberg, L. 43 105 139 242 244 246
Non-trapping condition 191
Noncharacteristic plane 26
Nonstrictly hyperbolic operator 26
Nonstrictly hyperbolic polynomial 26
Normal derivative lemma 86
Novikov, S.P 207 218
Numbers, defect 212
Oblique derivative problem 109
Olejnik, O.A. 132 165 167 168 171 173 176 177 242 245
Operator Cauchy — Riemann 20
Operator closed 211
Operator D'Alembertian 18
Operator elliptic 42
Operator elliptic at a point 42
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