Spectral and functional inequalities on antisymmetric functions

A. Laptev^ab, I. A. Shcherbakov<sup>b

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

Abstract: We obtain a number of spectral and functional inequalities related to Schrödinger operators defined on antisymmetric functions. Among them are Lieb — Thirring and CLR inequalities. Besides, we find new constants for the Sobolev and the Gagliardo — Nirenberg inequalities restricted to antisymmetric functions.

Keywords: Schrödinger operators, Lieb — Thirring and Cwikel — Lieb — Rozenblum inequalities, Sobolev and Hardy inequatilies, antisymmetric functions.

MSC: 35P15, 81Q10

Received: 21.11.2024

Language: English

 English version: Ufa Mathematical Journal, 2025, 17:1, 138–149