Extremum problems for Golubev sums期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

按检索

Extremum problems for Golubev sums

Authors:

S Ya Khavinson

Institution:

(1) Moscow Civil Engineering Institute, Moscow, USSR

Abstract:

Suppose thatG is a finitely connected domain with rectifiable boundary γ, ∞εG, the domainsD ₁,...,D _s are the complements ofG, the subsetsF _j ⊂D _j are infinite and compact,n _j≥1,j=1,...,s, are integers, λ₀ is a complex-valued measure on γ, and

$\omega _j (t) = \int_\gamma {(t - \xi )^{ - n_j } d\lambda _0 , t \in F_j } , j = 1,...,s.$

We consider the extremum problem

$\omega _j (t) = \int_\gamma {(t - \xi )^{ - n_j } d\lambda _0 , t \in F_j } , j = 1,...,s.$

where μ_j,j=1,...,s, are complex-valued measures onF _j and

$\left| {\sum\limits_{j = 1}^3 {\int_{F_j } {(t - z)^{ - n_j } d\mu _j } } } \right| \leqslant 1,$

are Golubev sums. We prove that β=Δ, where

$\vartriangle = \inf \int_\gamma {{{\left| {d\lambda } \right|} \mathord{\left/ {\vphantom {{\left| {d\lambda } \right|} {\int_\gamma {(t - \xi )^{ - n_j } d\lambda = \int_\gamma {(t - \xi )^{ - n_j } d\lambda _0 = \omega _j (t)} } , t \in F_j , j = 1, ..., s.}}} \right. \kern-\nulldelimiterspace} {\int_\gamma {(t - \xi )^{ - n_j } d\lambda = \int_\gamma {(t - \xi )^{ - n_j } d\lambda _0 = \omega _j (t)} } , t \in F_j , j = 1, ..., s.}}}$

We also establish several other relations between these and other extremal variables. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 738–745, May, 1999.

Keywords:

extremum problem analytic function rectifiable curve compact set Cauchy potential Golubev sum Laurent expansion complex-valued measure

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏