Lieb-Thirring inequality on the four-dimensional sphere and torus

Lieb-Thirring and Jensen sums for non-self-adjoint Schrödinger operators on the half-line

We prove upper and lower bounds for sums of eigenvalues of Lieb-Thirring type for non-self-adjoint Schrödinger operators on the half-line. The upper bounds are established for general classes of integrable potentials and are shown to be optimal in various senses by proving the lower bounds for specific potentials. We consider sums that correspond to both the critical and non-critical cases.

Lieb-Thirring inequalities and other functional inequalities for orthonormal systems

We review recent results on functional inequalities for systems of orthonormal functions. The key finding is that for various operators the orthonormality leads to a gain over a simple application of the triangle inequality. The operators under consideration are either related to Sobolev type inequalities or to Fourier restriction type inequalities.

A remark on a paper by Hundertmark and Simon

We prove a sharp Lieb-Thirring type inequality for Jacobi matrices, thereby settling a conjecture of Hundertmark and Simon. An interesting feature of the proof is that it employs a technique originally used by Hundertmark-Laptev-Weidl concerning sums of singular values for compact operators.

具有分形测度的正交 Sobolev 估计

Orthonormal Sobolev estimates with fractal measures

研究正交函数的分形 Hardy-Littlewood-Sobolev 不等式，通过傅里叶分析重证 Adams 不等式，避免 Schatten 类和变分论证，可恢复\(-\Delta - \mu\)负特征值相关界及负特征值之和的 Rozenblum 界。