翻訳と辞書
Words near each other
・ "O" Is for Outlaw
・ "O"-Jung.Ban.Hap.
・ "Ode-to-Napoleon" hexachord
・ "Oh Yeah!" Live
・ "Our Contemporary" regional art exhibition (Leningrad, 1975)
・ "P" Is for Peril
・ "Pimpernel" Smith
・ "Polish death camp" controversy
・ "Pro knigi" ("About books")
・ "Prosopa" Greek Television Awards
・ "Pussy Cats" Starring the Walkmen
・ "Q" Is for Quarry
・ "R" Is for Ricochet
・ "R" The King (2016 film)
・ "Rags" Ragland
・ ! (album)
・ ! (disambiguation)
・ !!
・ !!!
・ !!! (album)
・ !!Destroy-Oh-Boy!!
・ !Action Pact!
・ !Arriba! La Pachanga
・ !Hero
・ !Hero (album)
・ !Kung language
・ !Oka Tokat
・ !PAUS3
・ !T.O.O.H.!
・ !Women Art Revolution


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

Riemann–Hilbert factorization : ウィキペディア英語版
Riemann–Hilbert problem

In mathematics, Riemann–Hilbert problems, named after Bernhard Riemann and David Hilbert, are a class of problems that arise in the study of differential equations in the complex plane. Several existence theorems for Riemann–Hilbert problems have been produced by Krein, Gohberg and others (see the book by Clancey and Gohberg (1981)).
==The Riemann problem==
Suppose that Σ is a closed simple contour in the complex plane dividing the plane into two parts denoted by Σ+ (the inside) and Σ (the outside), determined by the index of the contour with respect to a point. The classical problem, considered in Riemann's PhD dissertation (see ), was that of finding a function
:M_+(z) = u(z) + i v(z)\!
analytic inside Σ+ such that the boundary values of ''M''+ along Σ satisfy the equation
:a(z)u(z) - b(z)v(z) = c(z) \!
for all ''z'' ∈ Σ, where ''a'', ''b'', and ''c'' are given real-valued functions .
By the Riemann mapping theorem, it suffices to consider the case when Σ is the unit circle . In this case, one may seek ''M''+(''z'') along with its Schwarz reflection:
:M_-(z) = \overline\right)}.
On the unit circle Σ, one has z = 1/\bar, and so
:M_-(z) = \overline,\quad z\in\Sigma.
Hence the problem reduces to finding a pair of functions ''M''+(''z'') and ''M''(''z'') analytic, respectively, on the inside and the outside of the unit disc, so that on the unit circle
:\fracM_+(z) + \fracM_-(z) = c(z),
and, moreover, so that the condition at infinity holds:
:\lim_M_-(z) = \bar_+(0).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Riemann–Hilbert problem」の詳細全文を読む



スポンサード リンク
翻訳と辞書 : 翻訳のためのインターネットリソース

Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.