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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Analytic Fredholm theorem ： ウィキペディア英語版 Analytic Fredholm theorem In mathematics, the analytic Fredholm theorem is a result concerning the existence of bounded inverses for a family of bounded linear operators on a Hilbert space. It is the basis of two classical and important theorems, the Fredholm alternative and the Hilbert–Schmidt theorem. The result is named after the Swedish mathematician Erik Ivar Fredholm. ==Statement of the theorem== Let ''G'' ⊆ C be a domain (an open and connected set). Let (''H'', ⟨ , ⟩) be a real or complex Hilbert space and let Lin(''H'') denote the space of bounded linear operators from ''H'' into itself; let I denote the identity operator. Let ''B'' : ''G'' → Lin(''H'') be a mapping such that * ''B'' is analytic on ''G'' in the sense that that the limit ::$\backslash lim\_)\}\{\backslash lambda\; -\; \backslash lambda\_\{0\}\}$ : exists for all ''λ''0 ∈ ''G''; and * the operator ''B''(''λ'') is a compact operator for each ''λ'' ∈ ''G''. Then either * (I − ''B''(''λ''))−1 does not exist for any ''λ'' ∈ ''G''; or * (I − ''B''(''λ''))−1 exists for every ''λ'' ∈ ''G'' \ ''S'', where ''S'' is a discrete subset of ''G'' (i.e., ''S'' has no limit points in ''G''). In this case, the function taking ''λ'' to (I − ''B''(''λ''))−1 is analytic on ''G'' \ ''S'' and, if ''λ'' ∈ ''S'', then the equation ::$B(\backslash lambda)\; \backslash psi\; =\; \backslash psi$ :has a finite-dimensional family of solutions. 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「Analytic Fredholm theorem」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.