Cordes H. — Elliptic Pseudo-Differential Operators - An Abstract Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Cordes H. — Elliptic Pseudo-Differential Operators - An Abstract Theory

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Название: Elliptic Pseudo-Differential Operators - An Abstract Theory

Автор: Cordes H.

Аннотация:

The present volume essentially is an edited version of the notes after the first two quarters of a lecture on partial differential equations held in 1976/77 at Berkeley. It represents an approach to theory of linear elliptic partial differential equations with emphasis on the abstract link between normal solvability of a linear operator and the structure of certain commutative С*-algebras, which are isomorphic to function algebras, by the Gel'fand-Nafmark theorem.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 331

Добавлена в каталог: 06.12.2009

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Предметный указатель

$C^{*}$ -algebra      319
$H_{\tau}$       66
$L^{2}$ -boundedness of integral operators      9
$t_{AS}$       69
$T_{ps}, T_{ra}$       61
Algebra $\Psi\nu$ of $\Psi do's$       141
Aperture topology      288
Apriori estimate      181
Associate dual map      290 313
Asymptotic expansion mod |x|      60 77
Asymptotic expansion mod |x| mod $O(-\infty)$       84 105
Asymptotic expansion mod |x| mod $Q(-\infty)$       119
Asymptotic expansion mod |x| mod D      60 70
Banach algebra (B-algebra)      291
Bessel function      291
Bessel potential      84
Boundary condition      193
Boundary problem      189
Calculus of $\Psi do's$       110
Calderon interpolation theorem      93
Cauchy principal value      59
Classical solution of a differential equation      18
Commutative B-algebra      303
Commutator relations      117
Compact operator      268
Compact order      108
Compactly supported distribution      34
Compactness of operators between F-spaces      142
Completely regular      315
Cone condition      187
Continuous linear functional      13
Convolution product      32 47
Cross norm      217
Dirac measure      61
Direct product      219 220
Dirichlet problem      181 196
distribution      11
Distribution with compact support      34
Distribution, derivative      15
Distribution, kernel      30
Distribution, solution of a differential equation      18
Dyad of order $-\infty$       123
Elliptic boundary problem      181 189 193
Elliptic boundary problem, $\Psi do$       127
Elliptic boundary problem, differential operator      81
Elliptic boundary problem, md-      128 140 194
Elliptic boundary problem, symbol      81
Euler's formula      67
Exponential growth      51
Finite part      59 66 67
Fourier distribution kernel      53
Fourier distribution kernel, integral      21
Fourier distribution kernel, kernel product      55
Fourier distribution kernel, Laplace transform      51
Fourier distribution kernel, multiplier      27 31
Fourier transform of a distribution      27
Fourier transform of a function      21 77
Fourier transform of a function depending on r only      26
Fourier transform of a polynomial      37
Fourier transform of an exponential function      37
Fourier transform of the delta function      36
Fredholm      254
Fredholm, closed      273
Fredholm, index      256
Fredholm, inverse      259
Fredholm, operator      254 258
Fredholm, operator between Banach spaces      263
Fredholm, pair      283
Fredholm, spectrum      140
Garding's inequality      129 184
Gel'fand theorem      308
Gel'fand — Naimark theorem      321
Green inverse      128 149 227
Hadamard's finite part      59
Half space      193
Hankel transform      26
Helmholtz equation      125
Herman's Lemma      137
Hilbert norm      5
Hilbert transform      95

Hoelder's inequality      5
Homogeneous distribution      66
Hyperfunction      2
Ideal      273 293
Integral operator, $L^{P}$ -boundedness of      9
Invertible mapping topology      287
Kernel multiplication      53
Kernel product      55
Kernel's Theorem      53 2
Laplace comparison algebra      127 129 199
Leibnitz' formula for $\Psi do's$       103
Leibnitz' formula for differential operators      9
Lifting of a symbol      142
Lipschitz condition      8
Local oscillation      122
Locally integrable function      12
Lopatinskij — Shapiro condition      194
M      73
Maximal ideal      303
Maximal ideal space      303
Maximum principle      125
Md-elliptic      128 140 194
Mellin convolution      182 204
Mellin transform      204
Multi-index notation      8
Neumann problem      195
Normally solvable      127 245 254
Order of a distribution      38
Order of an operator      83 99
Oscillation vanishing at $\infty$       84 119
Parseval's relation      31
Pointwise product      7 14
Postliminary algebra      182
Principal symbol space      127 157
Principal value      59
Product of distributions      14 30
Projection topology (for closed subspaces of a B-space)      287
Pseudo-differential operator $(\Psi do)$       83 101
Pseudo-function      61 63
Rational point      59 61
Rational point, singularity      59 61
Regular element      291
Rellich's criterion      268
Restriction of a distribution      15
Riesz ideal      273 5 5 5
Schmidt norm      77 292
Schur's lemma      9
Secondary symbol space      127
Semi — Fredholm operator      281
Semi-simple      309
Silov boundary      311
Singular integral operator      129 139 256
Singular support      16
Sobolev's inequality      186
Sobolev's inequality Lemma      86
Sobolev's inequality spaces      85
Special Fredholm inverse      259
Special Green inverse      227
Spectral family      185
Spectral family, radius      296
Spectrum      296
Stone — Weierstrass theorem      317
Strongly elliptic      129 181 184
Structure space(=maximal ideal space)      312
Support (of a distribution)      16
Symbol      127 195
Symbol of a differential operator      128
Symbol quotient      127 149
Symbol, space      127
Temperate distribution      27
Temperate distribution, function      29
Tensor product of a distribution of two Hilbert spaces      219 220
Topology for distribution spaces      38
Trace theorem      242
True order function      97
Ultra-distribution      2
Unbounded operator      276
Unsymmetric principal value      64
Wave front space      127
Wiener — Hopf convolution      181 200 201
Zero oscillation at      120

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