Brief communications

Spectral and functional inequalities for antisymmetric functions

A. A. Laptev^ab, I. A. Shcherbakov<sup>b

a</sup> Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom
^b Sirius Mathematics Center, Sirius University of Science and Technology, 1 Olympic Ave., Sochi, 354340 Russia

Abstract: A number of spectral and functional inequalities related to Schrödinger operators defined on antisymmetric functions is presented. Among them are Hardy and Sobolev inequalities, Lieb–Thirring and CLR inequalities.

Keywords: Schrödinger operator, Lieb–Thirring inequality, CLR inequality, Sobolev inequality, Hardy inequality, antisymmetric function.

UDC: 517.5

Received: 13.12.2024
Revised: 13.12.2024
Accepted: 18.12.2024

DOI: 10.26907/0021-3446-2025-2-104-109

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2025, 69:2, 77–82