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Egorov Y.V., Shubin M.A. — Partial Differential Equations I (Foundations of the Classical)
Egorov Y.V., Shubin M.A. — Partial Differential  Equations I  (Foundations of the Classical)

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Название: Partial Differential Equations I (Foundations of the Classical)

Авторы: Egorov Y.V., Shubin M.A.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 259

Добавлена в каталог: 10.09.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$H^{s}(\Omega)$      113
$H^{S}_{comp}(X)$      116
$H^{S}_{loc}(X)$      115
$S'(\Omega)$      49
$S(\Omega)$      48
$\mathcal{D'} (\Omega)$      50
$\mathcal{D} (\Omega)$      48
$\mathcal{E'} (\Omega)$      49
$\mathcal{E} (\Omega)$      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) $\overline{\partial}-$      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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