Power law logarithmic bounds of moments for long range operators in arbitrary dimension
Wencai Liu
TL;DR
This paper establishes explicit logarithmic bounds on the moments of long-range operators in any dimension, based on sublinear bounds of the Green's functions, advancing understanding of their spectral properties.
Contribution
It introduces a method linking Green's function bounds to moment bounds for long-range operators across arbitrary dimensions.
Findings
Logarithmic bounds of moments derived from Green's function bounds
Applicable to long-range operators in any dimension
Provides a new analytical approach for spectral analysis
Abstract
We show that the sublinear bound of the bad Green's functions implies explicit logarithmic bounds of moments for long range operators in arbitrary dimension.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Numerical methods in inverse problems · Holomorphic and Operator Theory