arXiv subjects

Zeguang Liu

Publications and source records attributed to Zeguang Liu.

3 recordsLinked to original sources

arXiv2026

The mixed spectral problem for radial Schr\"{o}dinger operators and Paley-Wiener spaces

The inverse spectral problem for the radial Schr\"{o}dinger operators on the finite interval is investigated. The potential is recovered from the given eigenvalues plus its information on a smaller interval. The method is to discuss the connections between the Paley-Wiener spaces and the potentials, from which we completely determine the potential on the whole interval from the potential on a smaller interval and a set of eigenvalues in terms of the complete exponential systems.

math.FA↗

arXiv2026

Deep zero problems and the HRT conjecture

We investigate a "deep zero problem" proposed by Hedenmalm. We show that there is a natural connection between Hedenmalm's problem and the classical HRT conjecture in time-frequency analysis. This connection allows us to show that Hedenmalm's problem 5.2 in [5] as well as some of its natural analogs have affirmative answers.

math.FA↗

arXiv2026

The inverse eigenvalue problems for perturbed Bessel operator with mixed data

We consider inverse eigenvalue problems for the perturbed Bessel operator in $L^{2}(0,1)$. (1) For the case where the angular-momentum quantum number $\ell\in\mathbb{N}\cup\{0\}$, we establish a uniqueness result for the inverse spectral problem by utilizing the closedness condition of a certain function system constructed based on the eigenvalues and the norming constants. (2) For the broader case where $\ell \geq -1/2$, we provide a uniqueness result for the inverse problem by using the density condition satisfied by the eigenvalues and the norming constants, where an additional smoothness condition may be imposed on the potential. (3) In the last section of this article, we present some corollaries based on (2). The results in these corollaries have already been established for the case $\ell=0$ by Gesztesy, Simon, Wei, Xu, Hatino\v{g}lu, et al., and we extend these results to the general case $\ell \geq -1/2$.

math.SP↗