Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
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Necessary and sufficient conditions are proven for Schrödinger operators to possess zero-energy bound states with bounded k-th position moments at the essential spectrum threshold.
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Weyl asymptotic formulas in the nilpotent Lie group setting
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
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Eigenstates with Infinite Position Moments
Necessary and sufficient conditions are proven for Schrödinger operators to possess zero-energy bound states with bounded k-th position moments at the essential spectrum threshold.