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| Natura: | Preprint |
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2023
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| Accesso online: | https://arxiv.org/abs/2305.06281 |
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| _version_ | 1866913998282162176 |
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| author | Qiu, Yaozhong W. |
| author_facet | Qiu, Yaozhong W. |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06281 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weyl asymptotics for functional difference operators with power to quadratic exponential potential Qiu, Yaozhong W. Spectral Theory Mathematical Physics Functional Analysis 34K08, 47A75 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. |
| title | Weyl asymptotics for functional difference operators with power to quadratic exponential potential |
| topic | Spectral Theory Mathematical Physics Functional Analysis 34K08, 47A75 |
| url | https://arxiv.org/abs/2305.06281 |