Weyl asymptotics for functional difference operators with power to quadratic exponential potential
File(s)
Accepted version
Author(s)
Qiu, Yaozhong
Type
Journal Article
Abstract
We continue the program first initiated in [LST16] 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 H0 = F−1Mcosh(ξ)F with potentials of the form W (x) = |x|p e|x|β for either β = 0 and p > 0 or β ∈ (0, 2] and p ≥ 0. We provide a new method for studying general potentials which includes the potentials studied in [LST16; LST19]. The proof involves dilating the variance of the gaussian defining the coherent state transform in a controlled manner preserving the expected asymptotics.
Riesz means and eigenvalue counting functions, of functional difference operators H0 = F−1Mcosh(ξ)F with potentials of the form W (x) = |x|p e|x|β for either β = 0 and p > 0 or β ∈ (0, 2] and p ≥ 0. We provide a new method for studying general potentials which includes the potentials studied in [LST16; LST19]. The proof involves dilating the variance of the gaussian defining the coherent state transform in a controlled manner preserving the expected asymptotics.
Date Issued
2024
Date Acceptance
2023-12-08
Citation
Proceedings of the American Mathematical Society, Series B, 2024, 152 (8), pp.3339-3351
ISSN
2330-1511
Publisher
American Mathematical Society
Start Page
3339
End Page
3351
Journal / Book Title
Proceedings of the American Mathematical Society, Series B
Volume
152
Issue
8
Copyright Statement
© Copyright 2024 American Mathematical Society This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (https://creativecommons.org/licenses/by-nc/4.0/).
License URL
Identifier
https://www.ams.org/journals/proc/2024-152-08/S0002-9939-2024-16765-4/?active=current
Publication Status
Published
Date Publish Online
2024-06-14