翻訳と辞書
Words near each other
・ Zeta Circini
・ Zeta Coronae Australis
・ Zeta Coronae Borealis
・ Zeta Corse
・ Zeta Corvi
・ Zeta Crateris
・ Zeta Crucis
・ Zeta Cygni
・ Zeta Delphini
・ Zeta Delta Xi
・ Zeta distribution
・ Zeta Doradus
・ Zeta Draconis
・ Zeta Equulei
・ Zeta Eridani
Zeta function (operator)
・ Zeta function regularization
・ Zeta function universality
・ Zeta Geminorum
・ Zeta Gruis
・ Zeta Herculis
・ Zeta Herculis Moving Group
・ Zeta Horologii
・ Zeta Hydrae
・ Zeta Hydri
・ Zeta Indi
・ Zeta Instrument Processor Interface
・ Zeta Interactive
・ Zeta Island, Bermuda
・ Zeta Leonis


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

Zeta function (operator) : ウィキペディア英語版
Zeta function (operator)
The zeta function of a mathematical operator \mathcal O is a function defined as
: \zeta_(s) = \operatorname \; \mathcal O^
for those values of ''s'' where this expression exists, and as an analytic continuation of this function for other values of ''s''. Here "tr" denotes a functional trace.
The zeta function may also be expressible as a spectral zeta function〔Lapidus & van Frankenhuijsen (2006) p.23〕 in terms of the eigenvalues \lambda_i of the operator \mathcal O by
: \zeta_(s) = \sum_ \lambda_i^ .
It is used in giving a rigorous definition to the functional determinant of an operator, which is given by
: \det \mathcal O := e^ \;.
The Minakshisundaram–Pleijel zeta function is an example, when the operator is the Laplacian of a compact Riemannian manifold.
One of the most important motivations for Arakelov theory is the zeta functions for operators with the method of heat kernels generalized algebro-geometrically.
==References==

*
*

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「Zeta function (operator)」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.