# Construction of dynamical semigroups by a functional regularisation \`{a} la Kato

## TL;DR

This paper introduces a functional regularisation method inspired by Kato's approach for constructing dynamical semigroup generators, applicable even when the unperturbed generator isn't positivity-preserving, demonstrated through a boson-number cut-off example.

## Contribution

It presents a new functional regularisation technique for dynamical semigroup generators that relaxes positivity-preservation requirements.

## Key findings

- Regularisation method successfully constructs generators without positivity constraints
- Application demonstrated via boson-number cut-off example
- Method broadens applicability of dynamical semigroup theory

## Abstract

A functional version of the Kato one-parametric regularisation for the construction of a dynamical semigroup generator of a relative bound one perturbation is introduced. It does not require that the minus generator of the unperturbed semigroup is a positivity preserving operator. The regularisation is illustrated by an example of a boson-number cut-off regularisation.