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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.06281 |
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Table of Contents:
- We continue the program first initiated in [Geom. Funct. Anal. 26, 288-305 (2016)] and develop a modification of the technique introduced in that paper to study the spectral asymptotics, namely the Riesz means and eigenvalue counting functions, of functional difference operators $\smash{H_0 = \mathcal F^{-1} M_{\cosh(ξ)} \mathcal F}$ with potentials of the form $\smash{W(x) = \lvert{x\rvert}^pe^{\lvert{x\rvert}^β}}$ for either $β= 0$ and $p > 0$ or $β\in (0, 2]$ and $p \geq 0$. We provide a new method for studying general potentials which includes the potentials studied in [Geom. Funct. Anal. 26, 288-305 (2016)] and [J. Math. Phys. 60, 103505 (2019)]. The proof involves dilating the variance of the gaussian defining the coherent state transform in a controlled manner preserving the expected asymptotics.