Thomas Hangelbroek

Associate Professor
Department of Mathematics
University of Hawaiʻi at Mānoa
2565 McCarthy Mall, Keller Hall 401A
Honolulu, HI 96822

Office: Physical Science Building 408
Email: hangelbr [at] math [dot] hawaii [dot] edu

Research Interests

My research lies at the interface of approximation theory, harmonic analysis and numerical analysis. I study kernels, radial basis functions, splines, and wavelets: i.e., basic tools for scattered data approximation, machine learning, and meshless solution of PDEs. I am interested in the approximation power of these tools, and in applying them to interesting problems.

Publications

My papers and preprints can be found on the arXiv.

Here are some recent ones:

T. Hangelbroek, C. Rieger, Smoothing by, and eccentric smoothing of, compactly supported RBFs , submitted

T. Hangelbroek, C. Rieger, G.B. Wright, Kernel approximation beyond the native space -- with applications to approximation on manifolds , submitted.

T. Hangelbroek, C. Rieger, G.B. Wright, Generalized local polynomial reproductions , to appear in Found. Comput. Math.

T. Hangelbroek, F. Narcowich, J. Ward, Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs , SIAM J. Numer. Anal. 64, (2026), no. 4, pp. 1539--1560.

T. Hangelbroek, C. Rieger, G.B. Wright, A Semi-Lagrangian scheme on embedded manifolds using generalized local polynomial reproductions , SIAM J. Numer. Anal. 64, (2026), no.3, pp. 853--875.

T. Hangelbroek, C. Rieger, G.B. Wright, Spectral stability and perturbation results for kernel differentiation matrices on the sphere , Numerische Mathematik 157, (2025), no. 2, pp. 505–538.

T. Hangelbroek, C. Rieger, Kernel Multigrid on Manifolds , J. Complexity 86 (2025), Paper No. 101900.

T. Hangelbroek, C. Rieger, Extending error bounds for radial basis function interpolation to measuring the error in higher order Sobolev norms , Math. Comp. 94, (2025), no. 351, pp. 381-407.

Upcoming travel

BIRS workshop on Kernel Approximation and Gaussian Processes: Integrating and Expanding Perspectives Sept 13-18, 2026. Co-organized with Janin Jäger, Cécile Piret, Christian Rieger, Grady Wright and me.

SIAM Conference on Mathematics of Data Science (MDS26) Nov 16-20, 2026 in Salt Lake City. Part of Varun Shankar and Grady Wright's minisymposium Recent Advances in Kernel Methods for PDEs and ML

Slides

Slides from talk I gave May 2026 at HU-Berlin on generalized local polynomial reproductions and semi-Lagrangian methods for PDEs on manifolds.

Slides from a presentation at WCCM-ECCOMAS'26 in July on Besov estimates for kernel approximation.

Teaching

Class Notes

Here are clasnotes for Math 633 -- Functional Analysis -- which I've taught periodically (most recently in Spring 2024).

You may also like these texts: Carl de Boor's Numerical Functional Analysis classnotes (which contain several nice problems, some of which I've borrowed), and books by Peter Lax, Hans Wilhelm Alt.

Links

UH Manoa Department of Mathematics
University of Hawaiʻi at Mānoa

Last updated: 2026