Currently, I am a 2nd Year PhD student under the supervision of Prof James RobisonLink opens in a new window, working on Lp convergence of eigenfunction expansions for second-order linear differential operators in the plane.
I may be reached at r.[last name A]-[last name B] at warwick.ac.uk.
In one dimension, there is only one way to truncate a partial sum: count up to a certain N. For eigenfunctions labelled by pairs of indices, as is the case of the Fourier series on Z2, we may truncate in several ways. For example, do we count pairs of indices (n, m) with |n|,|m| ≤ N, or instead count them with n2 + m2 ≤ N? It is a curious fact that Lp convergence can be obtained in the former case (for all p) but "never" the latter: it fails for all p ≠ 2! I am researching the Lp convergence of series of eigenfunctions on the disc, and equilateral, hemiequilateral and 45-90-45 triangles.
Praeterea, cum artis mathematicae operam non do, placet latine discere, legere, scribere ac loqui. (Plura de hoc sunt additura!)
|2020-2024 (Current)||CDT in Mathematical Sciences||University of Warwick|
|2019-2020||MASt in Matematical Sciences (Distinction)||University of Warwick|
|2015-2019||BSc (Hons) in Philosophy and Mathematics with Specialism in Foundations and Logic||University of Warwick|
|2021-2022||TA for MA3F1 Functional Analysis ILink opens in a new window and MA250 Introduction to PDELink opens in a new window|
|2020-2021||TA for MA359 Measure TheoryLink opens in a new window|
|2019-2020||TA for MA260 Norms, Metrics and TopologiesLink opens in a new window|
MA260 Support Classes
Here is some material I discussed during the Support Class for Norms, Metrics and Topologies:
DISCLAIMER: This material is my own and I take full responsibility for its content and any mistakes it may contain. It has not been revised by the lecturers or any other member of the department.
- R. L. Acosta Babb (2022) The Lp convergence of Fourier series on triangular domains. arXiv:2202.07641Link opens in a new window
- R. L . Acosta Babb (2022) Remarks on the Lp convergence of Bessel-Fourier series on the disc. arXiv:2202.06119Link opens in a new window
Notes and Slides
- Introductory notes on Complex Analysis (aimed at second year undergraduates with a bit of multivariable calculus)
- Topics in Harmonic Analysis (lecture notes written for a reading course in 2020-2021)
Talks and Conferences
- Guest speaker at "Universidade de Verán: MATEMÁTICAS: MOITO MÁIS QUE NÚMEROS!" , Universidade de Santiago de Compostela, 26-28 July, 2021.
Title: All functions are continuous! A provocative introduction to constructive analysis (Slides, no animations)
- What is the difference between a circle and a square?Link opens in a new window SPAAM Seminar Series (03/06/2021) at the University of Warwick.
This talk is an introduction to transference techniques which bridge the convergence of Fourier series and Fourier integrals.