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| Egorov Y.V., Shubin M.A. — Partial Differential Equations I (Foundations of the Classical) |
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| Предметный указатель |
 113
 116
 115
 49
 48
 50
 48
 49
 48
A priori estimate, internal 87
Abramowitz, M. 243
Absorption, limiting 189
Agmon's condition 112
Agmon, S. 105 112 243
Agranovich — Vishik condition 111
Agranovich, M.S. 5 111 132 140 243
Airy functions 236—237
Airy's equation 236—237
Airy, G.B. 236 238
Amplitude limiting 189
Amplitude scattering 193
Analytic singular support 63
Antiperiodic condition 206
Antiperiodic problem 206
Arithmetic sum of subsets 63
Arnol'd, V.I. 243
Arsenin, V.Ya. 21 247
Arzela, C. 103 120
Associated Legendre functions 221
Asymptotic completeness of wave operators 197
Atiyah, M. 150 243
Average 52
Balanced set 50
Balayage, method of 102
Banach, S. 23 51
Bateman, H. 243 244
Beltrami, E. 15 222
Berestetskij, V.B. 18 243
Berezanskij, Yu.M. 195 243
Berezin, F.A. 195 211 213 216 242 243
Bernshtejn's estimates 166
Bernshtejn, S.N. 166
Bers, L. 35 113 122 132 134 177 242 243
Besov, O.V. 113 121 242 243
Bessel functions of first kind 229
Bessel functions of imaginary argument 232
Bessel's equation 227—228
Bessel, F.W. 226—235
Bicharacteristic 46 191
Birman, M.Sh. 113 211 243
Bott, R. 150 244
Boundary condition(s) antiperiodic 206
Boundary condition(s) ellipticity 106
Boundary condition(s) ellipticity with parameter 111
Boundary condition(s) parabolicity 132
Boundary condition(s) periodic 206
Boundary condition(s) third 15
Boundary point, regular 102
Boundary-value problem 11
Boundary-value problem regularly elliptic 131
Boundary-value problem self-adjoint 131
Brelot, M. 100 102 243
Brillouin zone 219
Brillouin, L. 219
Bunyakovskij, V.Ya. 121 124 161
Capacity 101
Capacity inner 101
Capacity of a compact set 101
Capacity outer 101
Cauchy problem 22 24—27
Cauchy problem asymptotic solution of 153
Cauchy problem for an equation with constant coefficients 25
Cauchy problem for the heat equation 24 25
Cauchy problem for the one-dimensional wave equation 22
Cauchy problem fundamental solution of, for second-order equation with variable coefficients 171
Cauchy problem uniformly well-posed 179
Cauchy — Kovalevskaya Theorem 28—36
Cauchy — Riemann equations 20
Cauchy — Riemann operator 20
Cauchy — Riemann operator fundamental solution 70
Cauchy — Riemann system 20
Cauchy, A.L. 20 22—36 71—76 82 121 124 127 137—149 153 161 164 166 169—174 176—179 181 183 189 191 245
Characteristic 33
Characteristic direction 33
Characteristic surface 33
Charge 64
Chebyshev polynomials 238
Chebyshev, P.L. 238—239
Circle, Weyl limit- 214
Closed operator 211
Coddington, E.A. 207 243
Coefficient of reflection 218
Coefficient of transmission 218
Complementarity condition 107 175
Complete linearly independent system 200
Completeness of wave operators, asymptotic 197
Completeness of wave operators, asymptotic weak 196
Completeness sequential 51
Completeness weak 51
Condition(s) Agmon's 112
Condition(s) Agronovich — Vishik 111
Condition(s) boundary 11
Condition(s) boundary antiperiodic 206
Condition(s) boundary complementarity 107 175
Condition(s) boundary consistency 133
Condition(s) boundary covering 107
Condition(s) boundary Dirichlet 14
Condition(s) boundary ellipticity of 106
Condition(s) boundary ellipticity with parameter 111
Condition(s) boundary initial 11
Condition(s) boundary Neumann 14—15
Condition(s) boundary parabolicity of 132
Condition(s) boundary periodic 206
Condition(s) boundary Petrovskij well-posedness 27
Condition(s) boundary Shapiro — Lopatinskij 107
Condition(s) non-trapping 191
Condition(s) Sommerfeld radiation 185
Condition(s) third boundary 15
Cone, light 73
Conical refraction 157
Conjugate space 49
Consistency condition 132
Convergence uniform on compact sets, topology of 49
Convergence weak 51
Convolution of a distribution 63
Convolution of a function 63
Cook 196—197
Cook's criterion 197
Cook's method 196
Courant, R. 41 85 99 104 144 145 175 243 244
Covering condition 107
Criterion Cook's 197
Criterion Wiener's 103
Cylindrical function 226
Cylindrical function of second kind 231
d'Alembert's formula 22—23 141
D'Alembert, J. 18 19 22 72 142
d'Alembertian 18
D'Alembertian fundamental solution for 72
Darboux, G. 142
de Vries, G. 207
Defect index 212
Defect numbers 212
Defect subspace 212
Delta-function Dirac 47
Delta-function of a surface 64
Delta-shaped family of functions 51
Derivative of a distribution 55
Descent, method of 142
Differential operator, ordinary, fundamental solution for 70
| Differentiation of a distribution 55
Diffusion of waves 145
Dirac's equation 18
Dirac, P.A.M. 19 47 54
Direct product of distributions 61
Direct product of functions 61
Direction, characteristic 33
Dirichlet condition 14
Dirichlet integral 122
Dirichlet kernel 51
Dirichlet problem classical, solution of 104
Dirichlet problem exterior 93
Dirichlet problem for Laplace's equation 24
Dirichlet problem generalized statement of 123
Dirichlet problem interior 87
Dirichlet, L.P.G. 14 24 51 83 87 88
Discontinuity strong 155
Discontinuity weak 153
Discrete spectrum 17
Dispersion law 13
Distribution (Generalized Function) 48
Distribution convolution of 63
Distribution derivative of 55
Distribution homogeneous 59
Distribution regularization of 60
Distribution spherically symmetric 70
Distribution support of 53
Distribution tempered 49
Distribution tempered Fourier transform of 65
Double-layer potential 64 65
Douglis — Nirenberg ellipticity 43
Douglis, A. 43 105 189 242 244
Dual space 49
Duhamel, J.M.C. 75 144 181
Dunford, N. 243—244
Edwards, R.E. 47 51 242 244
Egorov, Yu.V. 34 244
Eidelman, S.D. 171 176 177 183 242 244
Eidus, D.M. 188 244
Eigenfunction 126
Eigenfunction Bloch 218
Eigenfunction of a continuous spectrum 194
Eigenvalue problem 126
Electrostatic equations 43
Elliptic cylinder functions 240
Elliptic equation 37
Elliptic equation at a point 37 42
Elliptic equation in a region 37 42 82
Elliptic operator at a point 37
Elliptic operator in a region 37
Elliptic operator Petrovskij- at a point 42
Elliptic operator Petrovskij- in a region 42 82
Ellipticity Douglis — Nirenberg 43
Ellipticity Petrovskij 42 82
Emde, F. 243 244
Energy estimates 161
Energy estimates, method of 138
Energy inequalities 159
Energy method 135
Energy zone 219
Energy, local 191
Equation(s)  20
Equation(s) Airy's 236—237
Equation(s) Bessel's 227—228
Equation(s) Cauchy — Riemann 20
Equation(s) Dirac's 18
Equation(s) electrostatic 43
Equation(s) elliptic 37
Equation(s) elliptic at a point 37 42
Equation(s) elliptic in a region 37 42 82
Equation(s) Euler — Poisson — Darboux 142
Equation(s) Euler's 221
Equation(s) Fredholm integral, of second kind 98
Equation(s) Hamilton — Jacobi 45
Equation(s) heat 10 37
Equation(s) Helmholtz' 15
Equation(s) hyperbolic 38
Equation(s) hyperbolic at a point 38
Equation(s) hyperbolic in a region 38
Equation(s) hyperbolic in the direction of a vector 43
Equation(s) hypergeometric 241
Equation(s) Klein-Gordon-Fock 18
Equation(s) Laplace's 14 37 220
Equation(s) Legendre's 225
Equation(s) linear partial differential 7
Equation(s) Mathieu's 240
Equation(s) Maxwell's 15—16
Equation(s) of Kovalevskaya type 28—29
Equation(s) of mixed type 38
Equation(s) parabolic 38
Equation(s) parabolic at a point 38
Equation(s) parabolic in a region 38
Equation(s) parabolic Petrovskij 2b- 44 163
Equation(s) parabolic Shilov- 163
Equation(s) Poisson's 14 83
Equation(s) Schroedinger 16 186
Equation(s) Schroedinger steady-state 17
Equation(s) telegraph 16
Equation(s) Tricomi 38
Equation(s) ultrahyperbolic 38
Equation(s) wave 37
Equation(s) wave multidimensional 12 37
Equation(s) wave one-dimensional 9
Erdelyi, A. 243 244
Eskin, G.I. 113 244
Essentially self-adjoint operator 211
Estimate, a priori internal 87
Estimates Bernshtejn's 166
Estimates energy 138
Estimates in Holder spaces 167
Estimates integral 166
Estimates Schauder 100
Euler — Poisson — Darboux equation 142
Euler's equation 221
Euler, L. 5 46 142 220 229 241
Example Hadamard's 21
Example Kreiss' 178
Exterior Dirichlet problem 93
Exterior Neumann problem 93
Faddeev, L.D. 218 244
Fedosov, B.V. 110 111 244
Fejer kernel 51
Flaschka — Strang theorem 138
Flaschka, G. 138 244
Floquet multiplier 219
Floquet, G. 218 219
Fock, V.A. 18
Forbidden zone 218
Formula(s) D'Alembert's 22—23 141
Formula(s) Green's 84
Formula(s) Green's second 85
Formula(s) Herglotz — Petrovskij 144
Formula(s) Kirchhoff's 142
Formula(s) Laplace's 226
Formula(s) Leibniz' 58
Formula(s) Mehler's 226
Formula(s) Poisson's 25 91 142 146 169
Formula(s) Rodrigues' 225
Formula(s) Sokhotskij's 52
Formula(s) Sommerfeld's 235
Fourier transform 65
Fourier transform method 142
Fourier transform of a function 65
Fourier transform of a tempered distribution 65
Fourier's method 135 163
Fourier, J.B.J. 10 162 169 194 197 198 201 210 235
Frechet space 23
Frechet, M.R. 23 47 49 50 115 116
Fredholm integral equation of second kind 98
Fredholm operator 109
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