Andersson M., Passare M., Sigurdsson R. — Complex convexity and analytic functionals :: Электронная библиотека попечительского совета мехмата МГУ

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Andersson M., Passare M., Sigurdsson R. — Complex convexity and analytic functionals

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Название: Complex convexity and analytic functionals

Авторы: Andersson M., Passare M., Sigurdsson R.

Аннотация:

A set in complex Euclidean space is called C-convex if all its intersections with complex lines are contractible, and it is said to be linearly convex if its complement is a union of complex hyperplanes. These notions are intermediates between ordinary geometric convexity and pseudoconvexity. Their importance was first manifested in the pioneering work of André Martineau from about forty years ago. Since then a large number of new related results have been obtained by many different mathematicians. The present book puts the modern theory of complex linear convexity on a solid footing, and gives a thorough and up-to-date survey of its current status. Applications include the Fantappié transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2004

Количество страниц: 160

Добавлена в каталог: 03.03.2006

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Предметный указатель

$\mathbb{C}$ -convex function      55
$\mathbb{C}$ -convex set      25
$\mathbb{C}$ -starlike set      32
$\mathcal{O}(E)$ -convex set      97
$\mathcal{O}(E)$ -convex support      97
Adjoint projective map      4
Affine line      3
Affinization      3
Analytic functional      93
Bochner — Martinelli formula      76
Borel transformation      133
Carrier      97
Cauchy — Fantappie — Leray, integral formula      76
Cauchy — Fantappie — Leray, kernel      74 90
Characteristic line      142
Complex projective space      5
Complex tangent space      51
Convex set      1 6
Defining function      50
Dual complement      16
Exponential solution      130
Fantappie transformation      107
Function of exponential type      132
Hartogs domain      53
hessian      50
Holomorphic hull      21
Holomorphically convex set      21 97
Homogeneous coordinates      3
Incidence manifold      89
Inverse Borel transform      133
k-homogeneous analytic functional      101
Kergin functional      122
Kergin polynomial      122
Laplace transformation      132
Levi form      50
Linear convexity      17

Linear fraction      23
Linearly convex hull      7 17 18
Linearly convex set      16 73
Linearly convex set in projective space      7
Newton interpolation formula      120
Non-degenerate $\mathbb{C}$ -convex set      25
Non-degenerate convex set      6
P-convexity for carriers      140
Parallel lines      3
Parallel planes      3
Polar of a convex set      2
Polar of a set in projective space      7
Polya — Ehrenpreis — Martineau theorem      139
Polynomial hull      22
Polynomially convex set      22
Projective hyperplane      2
Projective hyperplane at infinity      3
Projective k-plane      2
Projective line      2
Projective mapping      4
Pseudoconvex set      22
Real projective space      2
Real tangent space      51
Reinhardt set      27
Runge domain      22
Set of indeterminacy      4
Set of tangent hyperplanes      46
Simplex functional      95 102
Spirally connected set      65
Stein compact      113
Strictly $\mathbb{C}$ -convex set      52
Strong P-convexity for carriers      140
Supporting function      139
Tangent hyperplane      11 45
Topology of uniform convergence      76
Weakly linearly convex set      17

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