Phuoc-Tai Nguyen

collaborators

3 papers

math-ph2025

Finite-Rank Optimizers for the mass--supercritical Lieb--Thirring and Hardy--Lieb--Thirring Inequalities

Giao Ky Duong, Thi Minh Thao Le, Phan Thành Nam +1

We establish the existence of finite-rank operators for an interpolation version of the Lieb--Thirring inequality in the mass--supercritical case, thereby extending a result of Hon…

math-ph2023

Cwikel-Lieb-Rozenblum type inequalities for Hardy-Schrödinger operator

Giao Ky Duong, Rupert L. Frank, Thi Minh Thao Le +2

We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of the Hardy-Schrödinger operator $- Δ - (d - 2)^{2} / (4∣ x ∣^{2}) - W (x)$ on $L^{2} (R^{d})$ . The b…

math.AP2023

Semiclassical Moser-Trudinger inequalities

Rakesh Arora, Phan Thành Nam, Phuoc-Tai Nguyen

We extend the Moser-Trudinger inequality of one function to systems of orthogonal functions. Our results are asymptotically sharp when applied to the collective behavior of eigenfu…