Gilbert J., Murray M. — Clifford Algebras and Dirac Operators in Harmonic Analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Gilbert J., Murray M. — Clifford Algebras and Dirac Operators in Harmonic Analysis

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Название: Clifford Algebras and Dirac Operators in Harmonic Analysis

Авторы: Gilbert J., Murray M.

Аннотация:

The aim of this book is to unite the seemingly disparate topics of Clifford algebras, analysis on manifolds, and harmonic analysis. The authors show how algebra, geometry, and differential equations play a more fundamental role in Euclidean Fourier analysis. They then link their presentation of the Euclidean theory naturally to the representation theory of semi-simple Lie groups.

Язык:

Рубрика: Математика/Геометрия и топология/Дифференциальная геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 334

Добавлена в каталог: 03.06.2005

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Предметный указатель

Poisson transform      293
Polynomial representations of $GL(n, \mathbb R)$       163
Polynomials of matrix argument      173—193
Polynomials of matrix argument, determinantally homogeneous      174 182 184
Polynomials of matrix argument, SL(r)-invariant      180
Poor, W.      317
Porteous, I.R.      85
Principal anti-automorphism      17
Principal automorphism      17
Principal fiber bundle      264
Procesi, C.      201
Pseudo-scalar ()      24
Quadratic form      6
Quadratic space      6
Quadratic space, degenerate      7
Quadratic space, non-degenerate      7
Quadratic space, normalized basis for      7
Quadratic space, radical of      7 22
Quaternion-valued regular function      89
Quaternionic structure, on a complex G-module      146
Quaternions ( $\mathbb H$ )      9
Quillen, D.      296
Radical, of a quadratic space      7 22
Radon — Hurwitz numbers      206
Real projective space      266
Real spinor space      206
Real structure, on a complex G-module      146
Reduced products      11
Reflection      33
Representation theory, for $\mathrm{Spin}_0(n,1)$       284—296
Representation, finite dimensional      144
Representation, infinite dimensional      144
Representation, of a group      144
Representations of O(n)      162—163
Representations of SO(n)      162—163
Representations of SO(n), double-valued      162
Representations of SO(n), single-valued      162
Reproducing kernel property      91
reversion      18
Richards, D.St.P.      201
Riemannian curvature tensor      257
Riemannian metric, for spherical space      273
Riesz transforms      121
Rigid motion      35
Roe, J.      141 317—318
Rotation      35
Rotation, of $\mathbb R^n$       278
Rotation-invariant first-order systems      213—219
Rotation-invariant operators of Dirac type      215—219
Rotation-invariant operators, and Spin(n)-submodules      221
Schmid, W.      319
Schur's lemma      145
Schur, I.      145 163 179
Seeley, R.      319
Signature, of a representation      147 150—151
Similarity transformation      37
Singer, I.      244 311 318
Single layer potential; double layer potential      135—136
Slebarski, S.      318
Sommen, F.      141
Special Lipschitz domain, in $\mathbb R^n$       127
Spherical harmonics      165 225 228—230
Spherical harmonics, representations of SO(n) on      167—173
Spin group      46—49
Spin group, as a classical Lie group      77—84
Spin group, as a Lie group      65—84
Spin representations of Spin(n)      215
Spin structure, on a Riemannian manifold      268

Spin(n), complex      163
Spin(n), maximal abelian subgroup of      148
Spin(n), quaternionic      163
Spin(n), real      163
Spin(n), representations of      163
Spin(n), Weyl group of      150
Spin(V,Q)      46
Spinor Laplacian      259 262 306
Spinor space, complex      60
Spinor space, real      60
Spoin(V,Q)      47
Standard basis, for $\mathbb R^n$       51
Standard Dirac operator      96
Standard Dirac operator, ellipticity of      254
Standard Dirac operator, essential self-adjointness of      254
Standard Dirac operator, on a Riemannian manifold      250 253—254
Standard Dirac operator, on hyperbolic space      273
Standard Dirac operator, on spherical space      274
Standard Dirac operator, realizations of      99—100
Stein — Weiss $\overline\partial_\tau$ operators      222
Stein, E.M.      134 140—141 201 209 220 221 222 244 284 318
Stereographic projection      273—274
Structure map      146
Subharmonic function      91
Subharmonicity property, of a first-order system      233
Submodule, irreducible      144
Submodule, reducible      144
Supersymmetry      212
Supertrace      212 312—313 316
Symbol mapping, of $\eth_A$       205
Takahashi, R.      85 318
Tan $H^p(\mathbb R^{n-1})$       125
Taylor scries expansions      164—166 185—166
Tent space theory      134
tom Dieck, T.      85 201
Ton-That, T.      201
Total derivative, on a Riemannian manifold      270
Trace-harmonic function      195
Transformer      42
Transformers      42—45 275
Translation      35
Translation, of $\mathbb R^n$       278
Turnbull, H.      201
Twisted Dirac operator      211
Twisted spinor Laplacian      260—261
Two-fold covering      46
Uhlenbeck, K.      317
Ultraspherical polynomials      168
Unitary representation      145
Unitary representation, complex type      147
Unitary representation, real or quaternionic type      146—147
Universal Clifford algebra      12
Universal Clifford algebra, constructions of      13—17
Vagi, S.      141
Vahlen, K.      318
Vandermonde      190
Verchota, G.      137 141
Vergne, M.      318
Wallach, N.      318
Weak-type (1,1)      112
Weight, of a representation of Spin(n)      149
Weighted Hardy space      288
Weiss, G.      140 141 201 209 220 221 222 244 245
Weyl group element      279
Weyl group of Spin(n)      150
Weyl, H.      94 141 143 163 175 201
Witten, E.      318
Zygmund, A.      135 239

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