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| Egorov Y.V., Shubin M.A. — Partial Differential Equations I (Foundations of the Classical) |
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| Предметный указатель |
Operator elliptic in a region 42
Operator elliptic Petrovskij- 42
Operator essentially self-adjoint 211
Operator Fredholm 108
Operator Hill 218
Operator hyperbolic 26 27 137
Operator hyperbolic at a point 43 136
Operator hyperbolic in a region 43 136
Operator hyperbolic in the direction of a vector 43
Operator hyperbolic symmetric 157
Operator hypoelliptic 78
Operator infinitesimal generator 180
Operator Laplace — Beltrami 15
Operator Laplacian 10
Operator linear differential 7
Operator local 69
Operator maximal 212
Operator minimal 212
Operator monodromy 218
Operator nonstrictly hyperbolic 26
Operator ordinary differential, fundamental solution for 70
Operator properly elliptic 106
Operator scattering 195
Operator Schrodinger 17
Operator Schrodinger one-dimensional 202
Operator spectrum, discrete 17
Operator strictly hyperbolic 27
Operator strictly hyperbolic at a point 136
Operator strictly hyperbolic in a region 137
Operator strictly hyperbolic in the direction of a vector 43
Operator strictly hyperbolic Sturm — Liouville 201
Operator transposed 58
Operator wave 18 196
Order of an equation 7
Order of an operator 7
Outer capacity 101
Overdetermined system 42
Overdetermined system elliptic 42
Ovsyannikov's theorem 34
Ovsyannikov, L.V. 33 34
Palais, R.S. 113 242 246
Palamodov, V.P. 243 246
Paley — Wiener — Schwartz theorem 66
Paley, R.E.A.C. 24 66
Parabolic cylinder functions 240
Parabolic equation 38
Parabolic equation at a point 38
Parabolic equation in a region 38
Parabolic equation Petrovskij 2b- 44 163
Parabolic equation Shilov- 163
Parabolic system, Shilov- 172
Parabolicity, index of 172
Partial differential equation, linear 7
Pauli, W. 19
Peetre, J. 246
Periodic condition 206
Periodic Problem 206
Permitted zone 218
Petrovskij 2b-parabolic equation 44 163
Petrovskij ellipticity at a point 42
Petrovskij ellipticity in a region 42 82
Petrovskij, I.G. 27 29 35 42 82 83 85—87 94 97 144 145 150 163 172 177—179 242 246
Phillips, R. 140 184 199 244 245
Pitaevskij, L.P. 207 218
Planck, M. 17 187
Plane wave method 145
Plane wave scattering 192
Plane, noncharacteristic 26
Poincare, H. 18
Point regular boundary 103
Point Weyl limit- 214
Poisson's equation 14 83
Poisson's formula 25 91 142 146 169
Poisson, S.D. 14 25 72 88 91 99 142 169
Polynomial(s) Chebyshev 238
Polynomial(s) Chebyshev of first kind 238
Polynomial(s) Chebyshev of second kind 238
Polynomial(s) Hermite 239
Polynomial(s) hyperbolic 26
Polynomial(s) Laguerre 239
Polynomial(s) Legendre 144
Polynomial(s) nonstrictly hyperbolic 26
Potential double-layer 64 95
Potential heat 76
Potential Newtonian 63 94
Potential retarded 76
Potential single-layer 64 95
Potential volume 63 94
Principal symbol of a differential operator2 6 42
Principle Duhamel's 76 144
Principle Huyghens' 145
Principle maximum 24
Principle maximum for a general elliptic equation 104
Principle maximum for a parabolic equation 164
Principle maximum for harmonic functions 87
Principle maximum of limiting absorption 189
Principle maximum of limiting amplitude 189
Principle maximum strong 165
Problem  20
Problem antiperiodic 206
Problem boundary-value 11
Problem boundary-value regularly elliptic 131
Problem boundary-value self-adjoint 131
Problem Cauchy 22 24—27
Problem Cauchy for an equation with constant coefficients 25
Problem Cauchy for the heat equation 24 25
Problem Cauchy for the one-dimensional wave equation 22
Problem Cauchy uniformly well-posed 177
Problem Dirichlet 104
Problem Dirichlet exterior 93
Problem Dirichlet for Laplace's equation 24
Problem Dirichlet generalized statement 123
Problem Dirichlet interior 87
Problem eigenvalue 126
Problem mixed parabolic 132
Problem Neumann 87
Problem Neumann exterior 93
Problem Neumann generalized statement 123
Problem oblique derivative 109
Problem periodic 206
Problem regularly elliptic 131
Problem scattering 192
Problem self-adjoint 201
Problem self-adjoint regular 201
Problem Sturm — Liouville 202
Problem well-posed 24
Product direct of distributions 61
Product direct of functions 61
Product tensor of distributions 61
Product tensor of functions 61
Properly elliptic operator 106
Quasimomentum 219
Radiation condition, Sommerfeld 185
Radon measure 54
Radon transform 146
Radon, J. 54 146
Ray, geometric-optical 191
Rayleigh, J.W. 135
Reed, M. 199 204 211 242 246
Reflection, coefficient of 218
Refraction, conical 157
Regular boundary point 103
Regularization of a generalized function 52 60
Relations completeness 211
Relations orthogonality 210
Removable singularities theorem 81—82 92
Rempel, S. 110 111 242 246
Retarded potential 76
Riemann, G.F.B. 15 41 70 241
Riesz, F. 54 125
| Rodrigues' formula 225
Rodrigues, V.O. 225
Rolle, M. 225
Rudin, W. 23 47 51 53 65 242 246
Sakamoto, R. 246
Samarskij, A.A. 8 9 13 88 89 189 225 226 234 235 243 246
Sargsyan, I.S. 206 214 217 220 243 245
Scattering amplitude 193
Scattering matrix 198
Scattering of a plane wave 192
Scattering operator 195
Scattering problem 192
Schauder estimates 100
Schauder, J.P. 99 100
Schechter, M. 35 113 122 132 134 177 242 243
Schmidt, E. 204
Schrodinger, E. 16 17 19 150 182 186 196 202 210
Schroedinger equation 16 186
Schroedinger equation steady-state 17
Schroedinger operator 17
Schroedinger operator one-dimensional 202
Schulze, B.-W. 110 111 242 246
Schwartz kernel theorem 68
Schwartz space 48
Schwartz, J.T. 202 243 244
Schwartz, L. 24 47 51 53 55 57 65 66 68 242 246
Sears' theorem 213
Sears, D.B. 213
Seidenberg, A. 79
Self-adjoint problem 131
Semigroup, infinitesimal generator of 180
Separation of variables 135 163
Sequence, delta-shaped 51
Sequential completeness 51
Series, hypergeometric (Gauss') 241
Shapiro — Lopatinskij condition 107
Shapiro, Z.Ya. 105
Sheaf 53
Shilov, G.E. 47 51 53 55 57—59 62 65 69 71 73 78 83 132 163 164 172 242 244 246
Shilov-parabolic equation 163
Shubin, M.A. 195 211 213 216 242 243 246
Simon, B. 199 204 211 242 246
Single-layer potential 53
Singular integral 65
Singularity, weak 98
Smirnov, V.I. 88 90 94 97 242 243 246
Sobolev spaces 113
Sobolev spaces anisotropic 132
Sobolev spaces local 115
Sobolev, S.L. 24 113 117 119 131 243 246 247
Sokhotskij's formulas 52
Sokhotskij, Yu.B. 52
Solomyak, M.Z. 113 211 243
Solonnikov, V.A. 113 132 175 242 247
Solution fundamental 69
Solution fundamental for an operator 69
Solution fundamental for an ordinary differential operator 70
Solution fundamental for the Cauchy-Riemann operator 70
Solution fundamental for the D'Alembertian 72
Solution fundamental for the heat conduction operator 72
Solution fundamental for the Laplacian 70 83
Solution generalized (weak) 123
Solution generalized (weak) of a mixed boundary-value problem 161
Solution of a hyperbolic equation, discontinuous 153—157
Solution of the Cauchy problem 71 171
Solution of the Cauchy problem asymptotic 153
Solution of the Cauchy problem for second-order equation with variable coefficients 171
Solution of the classical Dirichlet problem 87
Solution of the Neumann problem 87
Solution weak (generalized) 123
Sommerfeld radiation condition 185
Sommerfeld's formula 235
Sommerfeld, A. 185 235
Source function for a Sturm — Liouville problem 202
Source function for the Dirichlet problem 88
Space(s)  48
Space(s)  50
Space(s)  48
Space(s)  49
Space(s)  48
Space(s)  49
Space(s) dual 49
Space(s) Frechet 23
Space(s) Hoelder 99
Space(s) of test functions 48
Space(s) Schwartz 48
Space(s) Sobolev 113
Space(s) Sobolev  116
Space(s) Sobolev  115
Space(s) Sobolev  113
Space(s) Sobolev anisotropic 132
Space(s) Sobolev local 115
Space-like 159
Special functions 220—241
Spectrum of an operator, discrete 17
Spherical harmonics 220
Stegun, I.A. 243
Stein, E.M. 243 247
Steinhaus, H.D. 51
Steklov's theorem 204—205
Steklov, V.A. 205
Stieltjes, T.J. 54
Stokes G.G. 68 84 128
Stone's theorem 182
Stone, A. 182
Strang, G. 138 244
Strictly hyperbolic operator, in the direction of a vector 43
Strictly hyperbolic system, in the direction of a vector 43
Strong discontinuity 155
Sturm — Liouville operator 201
Sturm — Liouville problem 202
Sturm's theorem 206
Sturm, J.C.F. 201 202 205 206
Subsets, arithmetic sum of 63
Subspace, defect 212
Sum of subsets, arithmetic 63
Support analytic singular 63
Support of a distribution 53
Support of a function 48
Surface characteristic 33
Surface space-like 159
Symbol, principal, of a differential operator 26 42
System Cauchy — Riemann 20
System complete linearly independent 200
System Douglis — Nirenberg elliptic 43
System Douglis — Nirenberg elliptic at a point 42
System Douglis — Nirenberg elliptic in a region 42
System Douglis — Nirenberg elliptic Petrovskij- 42
System Hamiltonian 191
System of electrostatic equations 43
System overdetermined 42
System overdetermined elliptic 42
System Shilov-parabolic 172
System strictly hyperbolic 43
System strictly hyperbolic in the direction of a vector 43
System symmetric hyperbolic 44
Tarski, A. 79
Taylor, B. 29
Taylor, J.R. 132 199 243 247
Telegraph equations 16
Tempered distribution 49
Tensor product of distributions 61
Tensor product of functions 61
Test functions 48
Theorem Cauchy — Kovalevskaya 28—36
Theorem Flaschka — Strang 138
Theorem Fredholm property, regularity of solutions, and an a priori estimate for elliptic problems 109
Theorem Garding's 137
Theorem Hadamard's 178
Theorem Harnack's 88
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