My research is mainly in Clifford analysis and harmonic analysis, with particular interests in monogenic functions, Dirac operators, special functions, Fourier analysis, spectral theory and approximation. A central part of my work has been the construction and study of higher-dimensional function systems, including Clifford prolate spheroidal wave functions, Clifford-Legendre polynomials and spherical monogenics. I am also interested in computational methods and in developing connections between Clifford analysis, approximation theory and related areas of applied and computational mathematics.

My PhD project was about the construction of multi-dimension prolate spheroidal wave functions and investigation of their properties. 

Some Notes

A simple note about Prolate Spheroidal Wave Functions (PSWFs) known as Slepian Functions.
Please let me know if there is a typo here.

You can reach the codes here.

https://github.com/HamedBaghal/One_Dimensional_PSWFs

https://doi.org/10.5281/zenodo.5651760

My Publications

Publications and Preprints

Published and Accepted

1. H. Baghal Ghaffari, J. A. Hogan and J. D. Lakey,
   Constructing Spherical Monogenics in R³.
   Accepted for publication in the ISAAC 2025 Congress proceedings.
   Preprint version: Constructing 3-Dimensional Monogenic Homogeneous Functions, arXiv:2406.04863.

2. H. Baghal Ghaffari, J. A. Hogan and J. D. Lakey,
   Clifford Prolate Spheroidal Wavefunctions and Associated Shift Frames.
   In Sampling, Approximation, and Signal Analysis: Harmonic Analysis in the Spirit of J. Rowland Higgins, Springer, pp. 393–411, 2024.
   DOI: 10.1007/978-3-031-41130-4_15.

3. H. Baghal Ghaffari, J. A. Hogan and J. D. Lakey,
   New Properties of Clifford Prolate Spheroidal Wave Functions.
   2023 International Conference on Sampling Theory and Applications (SampTA), Yale University, 2023.
   DOI: 10.1109/SampTA59647.2023.10301198.

4. H. Baghal Ghaffari, J. A. Hogan and J. D. Lakey,
   Properties of Clifford-Legendre Polynomials.
   Advances in Applied Clifford Algebras, 32, Article 12, 2022.
   DOI: 10.1007/s00006-021-01179-8.

5. H. Baghal Ghaffari, J. A. Hogan and J. D. Lakey,
   A Clifford Construction of Multidimensional Prolate Spheroidal Wave Functions.
   13th International Conference on Sampling Theory and Applications (SampTA), 2019.
   DOI: 10.1109/SampTA45681.2019.9030948.

Preprints

6. H. Baghal Ghaffari and A. Souabni,
   Expansion into Clifford Prolate Spheroidal Wave Functions.
   arXiv:2512.20646, 2025.

7. H. Baghal Ghaffari and S. Bernstein,
   Construction of Weighted Clifford Prolate Spheroidal Wave Functions.
   arXiv:2302.02748, 2023.

8. H. Baghal Ghaffari, J. A. Hogan and J. D. Lakey,
   Clifford Prolate Spheroidal Wave Functions.
   arXiv:2112.09897, 2021.

PhD Thesis

H. Baghal Ghaffari,
Higher-Dimensional Prolate Spheroidal Wave Functions.
PhD thesis, University of Newcastle, 2022.
Handle: 1959.13/1465850.

Current Research Projects

Generalization of the Complex Adjoint Matrix and Construction of Spherical Monogenics
Joint work with Jeffrey A. Hogan.

My Talks 

• Confirmation seminar about my Ph.D. proposal, At The University of Newcastle, (15/04/2019)

• Two-Dimensional Clifford Prolate Spheroidal Wave Functions, Technische Universität Bergakademie Freiberg, (Visiting) (01/07/2019)

• A Clifford Construction of Multidimensional Prolate Spheroidal Wave Functions, At The University of Bordeaux, (sampTa Conference) (12/07/2019)

• A Clifford Construction of Multidimensional Prolate Spheroidal Wave Functions, At The University of Aveiro, (ISAAC 2019 Conference) (01/08/2019)

• Construction of Multidimensional Prolate Spheroidal Wave Functions, At Monash University, (Austms Conference) (04/12/2019)

• Properties of higher-dimensional Clifford Prolate Spheroidal Wave Functions, At The University of New England, (Austms Conference) (09/12/2020)

• Higher Dimension Monogenic Functions by Reproducing Kernel and Optimization, At Ghent University, (ISAAC 2021 Congress) (04/08/2021)

• New Properties of Clifford Prolate Spheroidal Wave Functions, At The University of Newcastle, (Austms Conference) (09/12/2021)

• Clifford Prolate Spheroidal Wave Functions and Construction of the Spherical Monogenics, At Technische Universität Bergakademie Freiberg, (Visiting) (14/06/2022)

• Introduction to Clifford Analysis and Applications, At University of Tabriz, Faculty of Mathematical Sciences, Iran, Invited Talk (26/06/2024)

• Generalization of a Complex Adjoint Matrix to Construct Spherical Monogenics, At Nazarbayev University, (ISAAC 2025 Conference) (21/07/2025)

Poster Presentation

• A Clifford Construction of Multidimensional Prolate Spheroidal Wave Functions, At Polytechnic University of Turin, (ATFA conference) (June 25-27, 2019) The PDF of Poster

• Properties of Clifford Prolate Spheroidal Wave Functions, At STOBL22, (June 19-25, 2022) The PDF of Poster

• Properties of Clifford Prolate Spheroidal Wave Functions, At SampTa23 Conference, Yale University, New Haven, The United States, (July 10-14, 2023) The PDF of Poster (This is same as the Strobl22)

• Constructing Multidimensional Spherical Monogenics, At Strobl24, (June 09-15 June 2024) The PDF of Poster