Structure of eigenvalues and eigenfunctions
Lead Research Organisation:
University of Warwick
Department Name: Mathematics
Abstract
Fourier expansions are a key tool in the analysis of partial differential equations. Irregular functions can still be expanded as Fourier series, and then by truncating the Fourier series one obtains a sequence of smooth functions that converges to the original irregular function. This idea - and related techniques - forms a key part of many proofs in the area. However, truncated Fourier series - and, more generally, truncated eigenfunction expansions - may not converge in L^p for p not equal to 2, and this can prove problematic in many situations. Based on the observation that carefully chosen truncations of Fourier series do converge in L^p when p is not 2, this project will investigate how much this can be carried over the eigenfunction expansions in general domains (the Fourier series case corresponding to the Laplacian in a square domain). The results will be interesting in their own right, and should produce techniques useful in the analysis of a wide class of PDE models. The research lies in the area of Mathematical Analysis, with potential applications in the more theoretical aspects of Continuum Mechanics and Fluid dyanmics & aerodynamics.
Organisations
People |
ORCID iD |
James Robinson (Primary Supervisor) | |
Ryan Acosta Babb (Student) |
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/V520226/1 | 30/09/2020 | 31/10/2025 | |||
2443915 | Studentship | EP/V520226/1 | 04/10/2020 | 04/10/2024 | Ryan Acosta Babb |