Rempel S., Schulze B.-W. — Index Theory of Elliptic Boundary Problems :: Электронная библиотека попечительского совета мехмата МГУ

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Rempel S., Schulze B.-W. — Index Theory of Elliptic Boundary Problems

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Название: Index Theory of Elliptic Boundary Problems

Авторы: Rempel S., Schulze B.-W.

Аннотация:

Subject of this monograph are essential parts of the theory of boundary value problems for elliptic partial differential equations and pseudo-differential equations. The theory presented here is arranged with the consequent use of pseudo-differential operators and symbolic calculus.

Язык:

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 402

Добавлена в каталог: 03.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$C^{\infty}$ homotopy      78
$C^{\infty}$ parametrix      195
$L^{p}$ estimates      218
Adjoints of boundary problems      235
Agranovic — Dynin formula      254
Algebra with trace      307
Amplitude function      47
Analytical G-index      352
Analytical index      77
Analytical index formula      312 321
Asymptotic expansion      48
Atiyah — Singer index theorem      79
Banach space      15
Base      18
Bott element      33
Bott isomorphism      33
Bott periodicity      33 259
Boundary symbol      95 135 172 194 282 374
Boundary symbol of order m and type d      98 132
Bounded operator      13
Bundle isomorphism      18
Bundle morphism      18
Calderon — Seeley projector      213 241
Canonical elliptic family      308
Canonical elliptic tupel      309
Chern character      309
Classical elliptic boundary value problem      208
Classical PDO      62
Clutching construction      20
Clutching of boundary problems      214 256
Coarse index formula      302
Coboundary operator      29
Cocycle to a bundle      18
Cohomology spaces of a complex      272
Cokernel      13
Compact operator      14
Compatibility of symbols      134
Complementing conditions      209
Complete symbol      61
COMPLEX      31
Complex of operators      271
Complexification      20
Conormal bundle      25 53
Conormal variable      25
Continous homotopy      78
Cotangent bundle      22
Countable-normed space      94
Curvature form      308
de Rham complex      281
Degenerate boundary problems      323 326
Degenerate overdetermined problems      342
Degenerate problems for the biharmonic operator      339
Degenerate underdetermined problems      347
Density bundle      44
Difference bundle      26 29
Difference construction      27
Differentiable section      22
DIMENSION      13
Dirac distribution      39
Direct sum      19
Dirichlet problem      197 217
Dirichlet system      211
distribution      39
Distributional kernel      40
Distributional section      44
Dual bundle      20
Elementary complex      274
Elliptic boundary conditions      194
Elliptic boundary symbol      107
Elliptic boundary value problem      194
Elliptic complex      279 282
Elliptic differential operator      76
Elliptic operator      76 194 360
Elliptic operator matrix of Douglis — Nirenberg type      235
Elliptic regularity      77
Elliptic symbol      107 310
Elliptic tupel      307
Embedding theorem      47
Equivalence of complexes      31
Equivalence of operators      243
Equivalence of phase functions      54
Euler number      281
Excision function      48
Exterior product      19
External multiplication of operators      82
External multiplication of the K-theory      31
Families of Fredholm complexes      276
Formal symbol      290
Fourier distribution      55
Fourier transform      41
Fourier — Laplace transform      42
Frechet space      13
Fredholm alternative      237
Fredholm complex      272
Fredholm family      16
Fredholm operator      13
Fredholm pair      17 214
Frequency variable      52
G-invariant boundary problems      353
Global principal boundary symbol      172
Green formula      211 237
Green operator      59 143 171
Green symbol      96 373
Green symbol of Volterra type      373
Harmonic form      281
Hausdorff space      18
Hermitean adjoint operator      77
Hermitean metric      23
Hilbert space bundle      19
Hilbert — Schmidt norm      294
Hilbert — Schmidt operator      16 293
Hoelder estimates      218
Homogeneous principal symbol      62
Homotopy of complexes      31 274
Homotopy of symbols      78 246
Hopf bundle      21 34 261
INDEX      14 289 324 352 362
Index element      17 36
Index element belonging to a symbol      199 236 258
Index homomorphism      264

Index of a Fredholm complex      272 278 282
Index of a Fredholm pair      17
Index of an elliptic tupel      307
Index of degenerate problems      324
Index theorem      79 266 354
Interior boundary problem      324 331 362
Interior elliptic family      318
Interior symbol      135 194 282
Interpolation pair      46
Interpolation space      46
Inverse of boundary symbols      205
Isomorphy of complexes      31
John's identity      210
K-functor      25
Kernel      13
Lagrangean manifold      53
Laplace operators connected with a complex      279 281 283
Left parametrix      14 76 239
Leibniz rule      38 66
Length of a complex      31
Local representation of A      170
Manifold with boundary      24
Mapping cone      274
Mapping degree      21
Mixed problem for elliptic operators      367
Neighbouring manifold      24
Non-degenerate phase function      53
Normal boundary conditions      211
Oblique derivative problem      335
Operator of finite rank      14
Operator phase function      60
Operator symbol      68 133
Operator with $C^{\infty}$ kernel      61
Operators without the transmission property      354
Oscillatory integral      55
Overdetermined elliptic symbol      107
Overdetermined system      237
Parabolic boundary problem      367
Parabolic operator      370 371
Parametrix      14 76
Parametrix of a degenerate boundary problem      328
Parametrix of a Fredholm complex      272
Phase function      51
Poisson kernel      210
Positively homogeneous function      48
Potential condition      194
Potential operator      15 59 171
Potential symbol      95 125 373
Potential symbol of Volterra type      373
Principal symbol      290
Projection      18
Projective topology of the tensor product      112
Properly supported operator      41 59 146
Pseudo-differential operator      58 61 72
Pull back of bundles      20
Quasi-homogeneous symbols      368
Reduction of the order      79 104 222
Reduction to the boundary      252 323 330 335
Reduction to the interior boundary      329
Regularizer      14
Relative If-group      26
Restriction      18
Riemannian metric      24
Right parametrix      14 76 239
Root condition      209
s*-topology      39
Schwartz space      39
Section of a bundle      18
Shapiro — Lopatinski condition      195 213 242 323
Singular support      40
Smoothing Green operator      140
Smoothing operator      61 135 324
Smoothing operator of type d      171
Smoothing potential operator      140
Smoothing section      22
Smoothing trace operator      140
Sobolev problem      358
Sobolev space      42
Sobolev space parametrix      195
Space with base point      21
Stabilizing symbols      310
Stable equivalence of boundary problems      243
Stable equivalent      26
Stable homotopy of complexes      275
Stable homotopy of elliptic families      309
Structure group      19
Support      29 39 308
Support of a complex      31
Symbol      61
Symbol of A      291
Symmetry condition      123
Symplectic form      53
Tangent bundle      22
Temperate distributions      39
Tensor product      19 111
Thom Isomorphism      36
Topological G-index      352
Topological index      77 264
Trace class operator      16
Trace condition      194
Trace norm      292
Trace of an operator      16
Trace operator      59 143 171
Trace symbol      95 126 373
Trace symbol of Volterra type      373
Transition function      18
Transmission problems      363
Transmission property      118
Trivialization      18
Type of a Green symbol      97
Type of a trace symbol      96 126
Underdetermined elliptic symbol      107
Underdetermined system      237
Uniform a-priori estimates      212
Universality      112
Vector bundle      17
Volterra operator      369
w*-topology      41
Wave front set      40
Weakly bounded set      39
Wiener — Hopf operator      93

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