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Hormander L. — Notions of Convexity

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Название: Notions of Convexity

Автор: Hormander L.

Аннотация:

The first two chapters are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-) subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator.

Язык:

Рубрика: Математика/Геометрия и топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 414

Добавлена в каталог: 16.04.2005

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Предметный указатель

Affine      2 37 38
Analytic functional      300
Analytic set      213
Arithmetic mean      10
Barrier      173
Berezin's inequality      7
Birkhoff's theorem      46
Blaschke product      179
Bonnesen's inequality      82
Bony — Brezis lemma      379
Borel transform      304
Brunn — Minkowski's inequality      88
C convex      294
Capacitable set      213
Caratheodory's theorem      41
Carrier      301
Cauchy— Riemann eq.      248 251
Choquet's theorem      214
Commutator      396
Concave      1
Condition ( $\Psi$ )      379
Cone condition      220
Conjugate function      17 67
Continuity principle      207
Convex      1 36
Convex polyhedron      53
Cross ratio      99
Current      272
Defect      105
Dirichlet problem      118 172
Distance function      57
Domain of holomorphy      239
Doubly stochastic matrix      46
Dual cone      71
Epigraph      36
Extreme point      43
F. and M. Riesz theorem      181
Fantappie transform      306
Fenchel transform      67
Fenchel — Alexandrov theorem      82
Fourier — Laplace transform      112
Fundamental solution      117
G subharmonic      315 324
Gabriel's theorem      136
Gamma function      20
Gateau differential      55
Geometric mean      10
Grassmannian      319
Green's function      119
Hadamard's three circle th.      160
Hahn — Banach theorem      45
Hamilton vector      377
Hardy space      184 190
Harmonic function      116
Harmonic majorant      171
Harmonic mean      10
Harnack's inequality      123
Hausdorff's theorem      51
Helly's theorem      41
Hoelder's inequality      11
Hopf's maximum principle      122
Horn's theorem      49
Hyperbolic polynomial      63
I-symplectic      377
Indicator function      313
Inner factor      184

Integration current      274
inversion      118
Jensen's inequality      7
Josefson's theorem      286
Krein — Milman's theorem      44
Laplace equation      116
Laplace transform      301
Legendre transform      17 67
Lelong number      235 270 277
Levi form      228 244
Levi problem      239
Linearly convex      290
Liouville's theorem      160
Malgrange's theorem      333
Maximum principle      121
Mean value pr.      121 143 153 232
Minimal harmonic function      125
minimum modulus theorem      194
Minkowski's inequality      12
Minkowski's theorem      43 80
Mixed volume      77
Motzkin's theorem      62
Muirhead's theorem      47
Norm      57
Numerical range      52
Outer conormal bundle      376
Outer factor      184
P-convex      328 329
Permutation matrix      46
Perron's method      172
Pluriharmonic function      225
Pluripolar      285
Plurisubharmonic function      225
Poisson bracket      377
Poisson kernel      120
Poisson's equation      117
polar      70 203
Polarization      273 393
Positive cone      318
Positive current      272
Positive form      270 271
Potential      145
Projective convexity      99
Pseudo-convex      237 243 342
Quasi-convex function      27
R-Lagrangian      376
Relative boundary      42
Relative interior      42
Riesz — Herglotz' theorem      123
Runge domain      308
Schlicht function      160
Semi-convex function      26
Sheaf C      387
simplex      40
Singular factor      184
Siu's theorem      267 283
Starshaped      37
Strictly convex      6 56
Strictly pseudo-convex      243
Strong subadditivity      210
Subharmonic function      141
Superharmonic function      141
Supporting function      69
Titchmarsh's theorem      189
Trace measure      272
Weakly linearly convex      290
Wiman — Valiron's theorem      197

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