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VOL. 41 | 2004 Criticality of Generalized Schrödinger Operators and Differentiability of Spectral Functions
Masayoshi Takeda, Kaneharu Tsuchida

Editor(s) Hiroshi Kunita, Shinzo Watanabe, Yoichiro Takahashi

## Abstract

Let $\mu$ be a positive Radon measure in the Kato class. We consider the spectral bound $C(\lambda) = -\inf \sigma(\mathcal{H}^{\lambda \mu})\ (\lambda \in \mathbb{R}^1)$ of a generalized Schrödinger operator $\mathcal{H}^{\lambda \mu} = -\frac{1}{2} \Delta - \lambda \mu$ on $\mathbb{R}^d$, and show that the spectral bound is differentiable if $d \le 4$ and $\mu$ is Green-tight.

## Information

Published: 1 January 2004
First available in Project Euclid: 3 January 2019

zbMATH: 1063.60109
MathSciNet: MR2083718

Digital Object Identifier: 10.2969/aspm/04110333