Generalized Semigroups and Moderate Resolvent Conditions

Abstract

ABSTRACT We develop a generalized Hille–Yosida and perturbation framework for ‐semigroups in Colombeau‐type operator algebras. Starting from operator nets satisfying moderate resolvent bounds, we establish generation, stability under bounded and negligible perturbations, and resolvent estimates derived from dissipativity This extends classical semigroup methods to parameter‐dependent families with singular asymptotic behavior. Applications are given to regularized Schrödinger operators and to the heat equation with singular potential, recovering the Feynman–Kac semigroup in the generalized setting.