Egorov Y.V. (Ed), Shubin M.A. (Ed) — Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients :: Электронная библиотека попечительского совета мехмата МГУ

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Egorov Y.V. (Ed), Shubin M.A. (Ed) — Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients

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Название: Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients

Авторы: Egorov Y.V. (Ed), Shubin M.A. (Ed)

Аннотация:

The book contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 263

Добавлена в каталог: 13.09.2008

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Предметный указатель

Operator, properly supported pseudodifferential      14
Operator, pseudodifferential      7
Operator, semi-globally solvable pseudodifferential      63
Operator, singular integral      36
Operator, spectral function      108
Operator, Stein extension      238
Operator, strictly elliptic      167
Operator, subelliptic      65
Operator, transpose      8
Operator, uniformly elliptic pseudodifferential      32
Oshima, T.      73 118
Oshmyan, V.G.      96 113 114 118
Palais, R.S.      6 24 25 114 118
Palamodov, V.P.      250 251 254
Paley, R.E.A.C.      126 150 160 161 254
Paneyakh, B.P.      141 155 156 251 255
Parametrix      16
Parseval identity      151
Parseval theorem      152
Parseval, M.      36 151 152
Patodi, V.M.      109 114 115
Petkov, V.M.      101 119
Petrovskij class      244
Petrovskij criterion      244
Petrovskij criterion, local      244
Petrovskij cycle      247
Petrovskij, I.G.      114 119 125 127 180 203 212—215 217 219 228 231 233 234 237 240 242—247 250 252 254
Phase function      49
Phase function, Lagrangian manifold      58
Phase function, local      58
Phase function, non-degenerate      57
Plamenevskij, B.A.      114 119
Planck, M.      34
Plemelj, J.      155
Point of contact      74
Point of contact, higher order      74
Point of periodic flow      111
Point of stationary phase      79
Point, absolutely periodic      112
Point, diffractive      74
Point, elliptic boundary      74
Point, focal      82
Point, glancing      74
Point, gliding      74
Point, hyperbolic boundary      74
Point, non-critical      79
Point, non-degenerate      74
Poisson bracket      55
Poisson kernel      235
Poisson relation      111
Poisson, S.D.      33 40 55 111 112 125 144 149 234 235 237
Popov, G.S.      113 118
Potential, advanced      144
Potential, retarded      144
Povzner, A.Ya.      70 118
Principal homogeneous part of operator      178
Principal value of integral      13
Principle, courant's minimax      97
Prudnikov, A.P.      176 177 250 252
Pseudodifferential operator, complex powers      31
Pseudodifferential operator, kernel      7
Pseudolocality      8
Quantization      34
Quantization weyl      34
Radkevich, E.V.      114 118
Rauch, J.      67 119
Ray      82
Reed, M.      6 114 118 140 145 161 251 254
Regularization problem      168
Regularization, formal function      169
Relation, homogeneous canonical      60
Rempel, S.      6 107 114 119
Riemann, W.      184 218 227
Riesz, F.      23
Riesz, M.      125 127 168 172 198 202 250 254
Roitburd, V.      105
Root, $\alpha$ -well-posed      214
Root, Petrovskij well-defined      214
Root, stable      214
Root, unstable      214
Rossi, H.      159 251 253
Rozenblyum, G.B.      110 114
Rudin, W.      254
Safarov, Yu.G.      101 117
Sakamoto, R.      69 119
Samarskij, A.A.      146 171 251 255
Sato, M.      44 73 113 119
Schechter, M.      36 37 115
Schenk, D.      113 119

Schmidt, E.      18
Schrodinger, E.      103 113 145 147 212 220 225 227 238
Schulze, B.-W.      6 107 114 119
Schwartz, L.      8 35 51 59 125 127 134 137 138 141 160 250 254
Seely, R.T.      26 27 100 106 107 114 119
Seidenberg, A.      168 169 223 251
Semi-bicharacteristic, reflected property      71
Set, asymptotically space-like      138
Set, asymptotically time-like      138
Shapiro, Z.Ya.      222 232
Shatalov, V.E.      96 113 114 118
Shilov, G.E.      125—127 129 134—136 140 143 146 148 150 152 158 159 172 185 186 189 191 192 218—220 229 234 237 250 251 253 254
Shirkov, D.V.      126 127 144 206 251 252
Shubin, M.A.      4 6 8 9 13 14 16—19 26 32 35 37 46 48 66—68 85 90 96 99 101 105 109 110 113—116 119 181—184 251 255
Simon, B.      6 114 119 140 145 161 251 254
Singer, I.M.      25
Sobolev, S.L.      16 17 23 38 41 48 155 251 255
Sokhotskij, Yu.V.      155
Solomyak, M.Z.      110 114 115
Solution, asymptotic      83
Solution, rapidly oscillating      83
Sommerfeld, A.      146 171 251
Space, Schwartz      141
Space, test functions      128
Stein, E.M.      113 119 238
Sternberg, S.      44 79 96 114 117
Sternin, B.Yu.      96 113 114 118
Stieltjes, T.J.      109
Stojanov, L.      101 119
Structure, Symplectic      54
Sukharevskij, I.V.      70 119
Support of function      134
Support of generalized function      134
Support of generalized function singular      136
Swallow-tail      248
Symbol, classical      11
Symbol, convolution operator      108
Symbol, differential operator      6
Symbol, elliptic      15
Symbol, operator      102
Symbol, polyhomogeneous      11
Symbol, principal      11
Symbol, symmetric      34
Symbol, weyl      33
Tarski, A.      168 169 223 251
Taylor, B.      12 14 81 169 187 191
Taylor, M.E.      6 9 14 17 19 37 39 44 48 74 96 114 119
Theorem, Calderon      39
Theorem, Calderon — Zygmund      36
Theorem, composition      15
Theorem, Ikehara      109
Theorem, mean value      148
Theorem, Payley — Wiener      150
Theorem, regularity      17
Tikhonov, A.N.      146 171 251 255
Titchmarsh, E.      152 154 250 255
Transformation, canonical      54
Transformation, contact-      213
Transformation, Fourier      149
Transformation, fourier — laplace      175
Transformation, hilbert      13
Transformation, Laplace      176
Transformation, Lorentz      134
Treves, F.      6 9 14 17 19 39 40 41 44 48 96 111 114 119 168 185 251 255
Tulovskij, V.N.      105
Vajnberg, B.R.      79 90 95 113 119 146 171 251 255
Vandermonde, A.T.      87
Varchenko, A.N.      82 114 115 248—250 252 255
Vasil'ev, D.G.      101 113 119
Vasil'ev, V.A.      127 240 247 249 250 255
Vishik, M.I.      26 114 155 156 184 217 232 238 251 252 255
Vladimirov, V.S.      139 140 144—146 150 159—161 165 166 174 203 209 250 251 255
Volevich, L.R.      141 155 156 251 255
Volovoj, A.V.      113 119
Watson, G.N.      146 188 199 209 251 255
Wave diffusion      147 203
Wave front      82 180
Wave front of generalized function      180
Wave front of operator      243
Wave front set      44 48
Weak convergence      128
Wentzel, G.      78
Weyl h-symbol      34
Weyl symbol      33
Weyl, H.      33 34 100 102 103 105 184 255
Whittaker, E.T.      146 188 199 209 251 255
Wiener, N.      126 150 160 161 254
Yosida, K.      135 164 255
Young, T.      18
Zygmund, A.      36 113 115

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