Two dimensional delta Bose gas in a weighted space

TL;DR

This paper extends the mathematical framework of the two-dimensional delta Bose gas to a weighted space accommodating exponentially growing functions, and proves convergence of mollified models to the original semigroup.

Contribution

It introduces a weighted $L^2$ space for the delta Bose gas and establishes strong convergence of mollified semigroups to the true semigroup.

Findings

Extended the delta Bose gas semigroup to weighted spaces

Proved strong convergence of mollified models

Enabled analysis of exponentially growing functions

Abstract

We extend the construction of the semigroup of the two-dimensional delta-Bose gas in Gu, Quastel, and Tsai (2021) (based on Rajeev (1999) and Dimock and Rajeev (2004)) to a weighted $L^2$ space that allows exponentially growing functions. We further show that the semigroup of the mollified delta-Bose gas converges strongly to that of the delta-Bose gas.