Publications:
The non-Hermitian skin effect with three-dimensional long-range coupling, Habib Ammari, Silvio Barandun, Jinghao Cao*, Bryn Davies, Erik Orvehed Hiltunen, Ping Liu, Journal of the European Mathematical Society, 2024.
Exponentially localised interface eigenmodes in finite chains of resonators, Habib Ammari, Silvio Barandun, Bryn Davies, Erik Orvehed Hiltunen, Thea Kosche, Ping Liu*, Studies in Applied Mathematics, 2024.
A mathematical theory of super-resolution and two-point resolution, Ping Liu*, Habib Ammari, Forum of Mathematics, Sigma, 2024.
Stability of the non-Hermitian skin effect, Habib Ammari, Silvio Barandun, Bryn Davies, Erik Orvehed Hiltunen, Ping Liu*, SIAM Journal on Applied Mathematics, 84(4):1697-1717, 2024.
Mathematical foundation of sparsity-based multi-illumination super-resolution, Ping Liu*, Sanghyeon Yu, Ola Sabet, Lucas Pelkmans, and Habib Ammari, Applied and Computational Harmonic Analysis, 2024.
Super-resolution of positive near-colliding point sources, Ping Liu*, Habib Ammari, Information and Inference: a Journal of the IMA, 12(4):iaad048, 2023.
An Operator Theory for Analyzing the Resolution of Multi-illumination Imaging Modalities, Ping Liu*, Habib Ammari, SIAM Journal on Imaging Sciences, 16.4:2105–2143, 2023.
Improved resolution estimate for the two-dimensional super-resolution and a new algorithm for direction of arrival estimation with uniform rectangular array, Ping Liu*, Habib Ammari, Foundations of Computational Mathematics, pages 1-50, 2023.
Dynamic super-resolution in particle tracking problems, Ping Liu*, Habib Ammari, Applied and Computational Harmonic Analysis, 64:143-193, 2023.
A mathematical theory of computational resolution limit in one dimension, Ping Liu, Hai Zhang*, Applied and Computational Harmonic Analysis, 56:402-446, 2022.
A Mathematical Theory of Computational Resolution Limit in Multi-dimensional Spaces, Ping Liu, Hai Zhang*, Inverse Problems, 37(10):104001, 2021.
A Theory of Computational Resolution Limit for Line Spectral Estimation, Ping Liu, Hai Zhang*, IEEE Transactions on Information Theory, 67(7):4812-4827, 2021.
Preprints:
Applications of Chebyshev polynomials and Toeplitz theory to topological materials, Habib Ammari*, Silvio Barandun, Ping Liu, 2024.
Generalised Brillouin Zone for Non-Reciprocal Systems, Habib Ammari, Silvio Barandun, Ping Liu, Alexander Uhlmann*, 2024.
Tunable Localisation in Parity-Time-Symmetric Resonator Arrays with Imaginary Gauge Potentials, Habib Ammari, Silvio Barandun, Ping Liu, Alexander Uhlmann*, 2024, submitted to Forum of Mathematics, Sigma.
Spectra and pseudo-spectra theory of tridiagonal k-Toeplitz operators and the topological origin of the non-Hermitian skin effect, Habib Ammari, Silvio Barandun, Yannick De Bruijn, Ping Liu*, Clemens Thalhammer, 2024, submitted to SIAM Journal on Mathematical Analysis.
Perturbed block Toeplitz matrices and the non-Hermitian skin effect in dimer systems of subwavelength resonators, Habib Ammari, Silvio Barandun, Ping Liu*, submitted to Journal de Mathematiques Pures et Appliquees.
A mathematical theory of resolution limits for super-resolution of positive sources, Ping Liu*, Yanchen He, Habib Ammari
A measurement decoupling based fast algorithm for super-resolving point sources with multi-cluster structure, Ping Liu, Hai Zhang*, submitted to Inverse Problems.