A geometric criterion for strong linear convexity

Znamenskii, S. V.

doi:10.1007/bf01077495

Cited by 12 publications

(5 citation statements)

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“…Any C-convex domain is linearly convex, see [8], and the converse is true if D has C^-boundary, see [I], but not in general, see e.g. example 1 below.…”

Section: ** = E If E Is Compact (Open) Then E" Is Open (Compact) Andmentioning

confidence: 99%

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Cauchy-Fantappiè-Leray formulas with local sections and the inverse Fantappiè transform

Andersson¹

1992

Bul. Soc. Math. France

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“…Any C-convex domain is linearly convex, see [8], and the converse is true if D has C^-boundary, see [I], but not in general, see e.g. example 1 below.…”

Section: ** = E If E Is Compact (Open) Then E" Is Open (Compact) Andmentioning

confidence: 99%

“…This conjecture was announced by ZNAMENSKIJ in [8] to be true, and it is subject to a more elaborated treatment in [9], where the necessity of C-convexity is established. However, the proposed arguments for the sufficiency are long and involved and seem to have gaps.…”

Section: Introductionmentioning

confidence: 97%

Cauchy-Fantappiè-Leray formulas with local sections and the inverse Fantappiè transform

Andersson¹

1992

Bul. Soc. Math. France

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“…After the confirmation of the hypothesis [15,16] this condition was called the C-convexity [2,17,18]. It continues to attract attention as a natural complex analog of convexity:…”

Section: Introductionmentioning

confidence: 99%

The Closure and the Interior of C-convex Sets

Znamenskij

Znamenskii²

2019

Journal of Siberian Federal University. Mathematics &Amp; Physics

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C-convexity of the closure, interiors and their lineal convexity are considered for C-convex sets under additional conditions of boundedness and nonempty interiors. The following questions on closure and the interior of C-convex sets were tackled 1. The closure of a bounded C-convex domain may not be lineally-convex. 2. The closure of a non-empty interior of a C-convex compact in Cn may not coincide with the original compact. 3. The interior of the closure of a bounded C-convex domain always coincides with the domain itself. The questions were formulated by Yu. B. Zelinsky

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“…[2,8,25]). However, representing analytic functionals as analytic functions on domains in C n requires specific tools of the general theory of partial differential equations (cf.…”

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confidence: 99%

Duality by reproducing kernels

Shlapunov¹,

Тарханов

2003

International Journal of Mathematics and Mathematical Sciences

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Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write A (Ᏸ) for the space of solutions of the system Au = 0 in a domain Ᏸ X. Using reproducing kernels related to various Hilbert structures on subspaces of A (Ᏸ), we show explicit identifications of the dual spaces. To prove the regularity of reproducing kernels up to the boundary of Ᏸ, we specify them as resolution operators of abstract Neumann problems. The matter thus reduces to a regularity theorem for the Neumann problem, a well-known example being the∂-Neumann problem. The duality itself takes place only for those domains Ᏸ which possess certain convexity properties with respect to A.

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A geometric criterion for strong linear convexity

Cited by 12 publications

References 0 publications

Cauchy-Fantappiè-Leray formulas with local sections and the inverse Fantappiè transform

Cauchy-Fantappiè-Leray formulas with local sections and the inverse Fantappiè transform

The Closure and the Interior of C-convex Sets

Duality by reproducing kernels

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