Rupert L. Frank

collaborators

5 papers

math.FA2024

Endpoint Schatten class properties of commutators

Rupert L. Frank, Fedor Sukochev, Dmitriy Zanin

We study trace ideal properties of the commutators $[(- Δ)^{\frac{ε}{2}}, M_{f}]$ of a power of the Laplacian with the multiplication operator by a function $f$ on $R^{d}$ . For a c…

math-ph2024

Lieb-Thirring inequality for the 2D Pauli operator

Rupert L. Frank, Hynek Kovařík

By the Aharonov-Casher theorem, the Pauli operator $P$ has no zero eigenvalue when the normalized magnetic flux $α$ satisfies $∣ α ∣ < 1$ , but it does have a zero energy resonance. We…

math.AP2024

Hardy inequalities for large fermionic systems

Rupert L. Frank, Thomas Hoffmann-Ostenhof, Ari Laptev +1

Given $0 < s < \frac{d}{2}$ with $s \leq 1$ , we are interested in the large $N$ -behavior of the optimal constant $κ_{N}$ in the Hardy inequality $\sum_{n=1}^N (-Δ_n)^s \geq κ_N \sum_{n<m} |X…

math.AP2024

On the sharp constants in the regional fractional Sobolev inequalities

Rupert L. Frank, Tianling Jin, Wei Wang

In this paper, we study the sharp constants in fractional Sobolev inequalities associated with the regional fractional Laplacian in domains.

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…