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Sub-exponential decay of operator kernels for functions of generalized Schrödinger operators. (English) Zbl 1053.81028
The paper is devoted to the improvement of the authors’ previous paper [F. Germinet and A. Klei, Proc. Am. Math. Soc. 131, No. 3, 911–920 (2003; Zbl 1013.81009)]. Let $$H$$ be a generalized Schrödinger operator on $$L^2(\mathbb{R}^d, dq;\mathbb{C}^k)$$. The following inequality $\| \chi_xf(H)\chi_y\| \leq C\exp(-c| x-y| ^\alpha), \;\;\;x,y\in\mathbb{R}^d,$ is proved for $$C^\infty$$ functions $$f$$ belonging to a $$L^1$$-Gervey class. Here $$\alpha\in(0,1]$$ is depending on $$f$$, and $$\chi_x(q)=\chi_0(q-x)$$, $$x,q\in\mathbb{R}^d$$, where $$\chi_0$$ is the characteristic function of the cube centered at 0 with side 1.

##### MSC:
 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX) 35P05 General topics in linear spectral theory for PDEs
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