# Reduction of dimension as a consequence of norm-resolvent convergence and applications

## TL;DR

This paper develops a unified framework for dimensional reduction using norm resolvent convergence, providing explicit bounds and spectral asymptotics, and applies it to various PDE problems in mathematical physics.

## Contribution

It introduces a general method for dimensional reduction via norm resolvent convergence, unifying and extending previous results across different PDE contexts.

## Key findings

- Derived explicit bounds on resolvent differences
- Established spectral asymptotics for reduced models
- Unified analysis of diverse PDE problems

## Abstract

This paper is devoted to dimensional reductions via the norm resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral asymptotics. The efficiency of our abstract tool is demonstrated by its application on seemingly different PDE problems from various areas of mathematical physics; all are analysed in a unified manner now, known results are recovered and new ones established.