An optimal<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-bound on the Krein spectral shift function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

An optimalLp-bound on the Krein spectral shift function

Authors:

Dirk?Hundertmark author-information" > author-information__contact u-icon-before" > mailto:dirkh@caltech.edu" title=" dirkh@caltech.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Barry?Simon

Affiliation:

(1) Department of Mathematics 253-37, California Institute of Technology, 91125 Pasadena, CA, USA

Abstract:

Let ξ_A,B be the Krein spectral shift function for a pair of operatorsA, B, with C =A-B trace class. We establish the bound

$int {F(|xi _{A,B} (lambda )|)} dlambda leqslant int {F(|xi _{|C|,0} (lambda )|)} dlambda = sumlimits_{j = 1}^infty {[F(j) - F(j - 1)]mu _j (C),}$

whereF is any non-negative convex function on [0, ∞) with F(0) = 0 and Ώ_j (C) are the singular values ofC. The choice F(t) =t ^p,p ≥ 1, improves a recent bound of Combes, Hislop and Nakamura. Supported in part by NSF grant DMS-9707661.

Keywords:

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