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Curriculum Vitae — Research Profile
Research & Publications — Vignon S. Oussa
My research centers on harmonic analysis on Lie groups,
frame theory and time–frequency analysis (including the HRT conjecture),
representation theory and sampling, and
algorithmic Lie theory, with additional work in
applied mathematical modeling.
This revised page foregrounds a bibliography-first structure so that published papers,
proceedings, and publicly posted preprints are easier to verify and less likely to be omitted.
The search filters rows in the bibliography tables below.
Research Areas & Expertise
The table below summarizes the principal mathematical areas represented in the bibliography.
| Area of Expertise | Focus & Typical Questions |
|---|---|
| Harmonic Analysis on Lie Groups | Nilpotent and exponential solvable Lie groups; band-limited spaces; admissibility; sampling and interpolation; orbit methods and representation-theoretic constructions. |
| Frame Theory & Time–Frequency Analysis | Frames, Riesz bases, Gabor systems, wavelet systems, robustness to erasures, full-spark phenomena, and orbit-generated systems on Euclidean and non-Euclidean settings. |
| Representation Theory & Sampling | Irreducible, quasiregular, and monomial representations; decomposition problems; sampling theorems on Lie groups and related representation-theoretic models. |
| HRT Conjecture & Phase Retrieval | Linear independence of time–frequency translates, Zak-transform methods, Heisenberg-group formulations, special configurations, and phase retrieval for Lie and finite groups. |
| Algorithmic Lie Theory & Computation | Computation of Lie algebras and polarizing subalgebras; Mathematica implementations; symbolic and structural algorithms motivated by representation theory. |
| Applied Mathematics & Modeling | Optimal control models in cancer therapy and tumor anti-angiogenesis, including treatment-cost penalties and related qualitative analysis. |
Representative Highlights
A short cross-section of representative work across the main themes.
| Area | Representative Citation |
|---|---|
| Harmonic Analysis on Lie Groups | V. Oussa, “Orthonormal bases arising from nilpotent actions,” Trans. Amer. Math. Soc. 377(2) (2024), 1141–1181. |
| Time–Frequency Analysis / HRT | K. A. Okoudjou and V. Oussa, “The HRT conjecture for two classes of special configurations,” J. Fourier Anal. Appl. 31 (2025), no. 4, Paper No. 48, 2 pp. |
| Phase Retrieval | H. Führ and V. Oussa, “Phase Retrieval for Nilpotent Groups,” J. Fourier Anal. Appl. 29 (2023), Art. 47. |
| Frames on Groups | H. Führ and V. Oussa, “Groups with frames of translates,” Colloq. Math. 167 (2022), 73–91. |
| Exponential Bases & Frames | J.-P. Gabardo, C.-K. Lai, and V. Oussa, “On Exponential Bases and Frames with Non-linear Phase Functions and Some Applications,” J. Fourier Anal. Appl. 27 (2021), Art. 9. |
| Algorithmic Lie Theory | Computing a Lie Algebra from a Generating Set I and Elementary Algorithms for Lie Algebras in Mathematica with Synthetic Data. |
| Applied Mathematics | U. Ledzewicz, V. Oussa, and H. Schättler, “Optimal solutions for a model of tumor anti-angiogenesis with a penalty on the cost of treatment,” Applicationes Mathematicae 36(3) (2009), 295–312. |
Monograph
| Year | Citation | Details |
|---|---|---|
| 2025 |
V. Oussa, A Bridge Between Lie Theory and Frame Theory: Applications of Lie Theory to Harmonic Analysis . |
Wiley, 2025. Print ISBN: 978-1-119-71213-8; Online ISBN: 978-1-119-71216-9. Monograph |
Refereed Journal Articles
This section consolidates the peer-reviewed journal bibliography into a single table, sorted from most recent to earliest.
| Year | Area | Citation / Link |
|---|---|---|
| 2025 | Time–Frequency Analysis / HRT | K. A. Okoudjou and V. Oussa, “The HRT conjecture for two classes of special configurations,” J. Fourier Anal. Appl. 31 (2025), no. 4, Paper No. 48, 2 pp. arXiv |
| 2024 | Harmonic Analysis on Lie Groups | V. Oussa, “Orthonormal bases arising from nilpotent actions,” Trans. Amer. Math. Soc. 377(2) (2024), 1141–1181. publisher link |
| 2023 | Phase Retrieval / Representation Theory | H. Führ and V. Oussa, “Phase Retrieval for Nilpotent Groups,” J. Fourier Anal. Appl. 29 (2023), Art. 47. DOI |
| 2023 | Phase Retrieval / Finite Groups | D. Bartusel, H. Führ, and V. Oussa, “Phase retrieval for affine groups over prime fields,” Linear Algebra Appl. 677 (2023), 161–193. DOI |
| 2022 | Frames on Groups / Harmonic Analysis | H. Führ and V. Oussa, “Groups with frames of translates,” Colloq. Math. 167 (2022), 73–91. DOI |
| 2022 | Finite Frames / Group Orbits | S. Maniscalco and V. Oussa, “Full-spark frames arising from one-parameter groups,” Linear Multilinear Algebra 70(16) (2022), 3031–3053. journal issue |
| 2021 | Exponential Bases & Frames | J.-P. Gabardo, C.-K. Lai, and V. Oussa, “On Exponential Bases and Frames with Non-linear Phase Functions and Some Applications,” J. Fourier Anal. Appl. 27 (2021), Art. 9. DOI |
| 2021 | Probability on Groups | V. Oussa, “Random walk on finite extensions of lattices,” Adv. Pure Appl. Math. 12(1) (2021), 63–78. DOI |
| 2020 | Finite Frames / Representation Theory | R. D. Malikiosis and V. Oussa, “Full spark frames in the orbit of a representation,” Appl. Comput. Harmon. Anal. 49(3) (2020), 791–814. DOI |
| 2020 | HRT / Heisenberg Group | B. Currey and V. Oussa, “Translates of Functions on the Heisenberg Group and the HRT Conjecture,” Canad. Math. Bull. 63(4) (2020), 871–881. DOI |
| 2019 | Frames on Lie Groups | V. Oussa, “Compactly supported bounded frames on Lie groups,” J. Funct. Anal. 277(6) (2019), 1718–1762. DOI |
| 2019 | Continuous Wavelets | B. Currey, H. Führ, and V. Oussa, “A classification of continuous wavelet transforms in dimension three,” Appl. Comput. Harmon. Anal. 46(3) (2019), 500–543. DOI |
| 2018 | Frames from Solvable Actions | V. Oussa, “Frames arising from irreducible solvable actions I,” J. Funct. Anal. 274(4) (2018), 1202–1254. DOI |
| 2018 | Gabor Theory / Geometry | H. Burgiel and V. Oussa, “Gabor orthonormal bases generated by indicator functions of parallelepiped-shaped sets,” Adv. Pure Appl. Math. 9(2) (2018), 93–107. research page |
| 2018 | Finite Frames / Haar Property | V. Oussa and B. Sheehan, “Dihedral group frames with the Haar property,” Linear Multilinear Algebra 66(6) (2018), 1121–1132. DOI |
| 2016 | Representation Theory / Group Actions | D. Arnal, B. Currey, and V. Oussa, “Characterization of Regularity for a Connected Abelian Action,” Monatsh. Math. 180(1) (2016), 1–37. DOI |
| 2016 | Sampling on Nilpotent Lie Groups | V. Oussa, “Sampling and Interpolation on Some Nilpotent Lie Groups,” Forum Math. 28(2) (2016), 255–273. DOI |
| 2015 | Algorithmic Lie Theory | V. Oussa, “Computing Vergne Polarizing Subalgebras,” Linear Multilinear Algebra 63(3) (2015), 578–585. DOI |
| 2015 | Finite Frames / Erasures | V. Oussa, “Dihedral Group Frames which are Maximally Robust to Erasures,” Linear Multilinear Algebra 63(12) (2015), 2494–2510. DOI |
| 2015 | Geometry / Lattices | H. Burgiel and V. Oussa, “Pairs of Full-Rank Lattices with Parallelepiped-Shaped Common Fundamental Domains” (published; public version available via arXiv). faculty record |
| 2014 | Time–Frequency Groups | A. Mayeli and V. Oussa, “Regular Representations of Time-frequency Groups,” Math. Nachr. 287(11–12) (2014), 1320–1340. DOI |
| 2014 | Shift-Invariant Spaces | B. Currey, A. Mayeli, and V. Oussa, “Characterization of Shift-Invariant Spaces on a Class of Nilpotent Lie Groups with Applications,” J. Fourier Anal. Appl. 20(2) (2014), 384–400. DOI |
| 2014 | Band-limited Spaces on Lie Groups | V. Oussa, “Bandlimited Spaces on Some 2-step Nilpotent Lie Groups with One Parseval Frame Generator,” Rocky Mountain J. Math. 44(4) (2014), 1343–1366. DOI |
| 2014 | Sinc-Type Systems / Nilpotent Groups | V. Oussa, “Sinc-type Functions on a Class of Nilpotent Lie Groups,” Adv. Pure Appl. Math. 5(1) (2014), 5–19. DOI |
| 2013 | Admissibility / Solvable Lie Groups | V. Oussa, “Admissibility for Quasiregular Representations of Exponential Solvable Lie Groups,” Colloq. Math. 131(2) (2013), 241–264. DOI |
| 2013 | Linear Independence / Dilations | D. Ferrone and V. Oussa, “Linear Independence of a Finite Set of Dilations by a One-parameter Matrix Lie Group,” Int. J. Pure Appl. Math. 84(2) (2013), 49–62. DOI |
| 2013 | Wavelet Frames on Nilpotent Groups | V. Oussa, “Shannon-like Parseval Frame Wavelets on Some Two step Nilpotent Lie Groups,” Int. J. Pure Appl. Math. 84(4) (2013), 397–418. DOI |
| 2012 | Admissibility / Representation Theory | B. Currey and V. Oussa, “Admissibility for Monomial Representations of Exponential Lie Groups,” J. Lie Theory 22(2) (2012), 481–487. arXiv |
| 2009 | Optimal Control / Mathematical Biology | U. Ledzewicz, V. Oussa, and H. Schättler, “Optimal solutions for a model of tumor anti-angiogenesis with a penalty on the cost of treatment,” Applicationes Mathematicae 36(3) (2009), 295–312. DOI |
| 2009 | Optimal Control / Mathematical Biology | U. Ledzewicz, V. Oussa, and H. Schättler, “Model for cancer therapy with penalty on the cost of treatment,” Int. J. Pure Appl. Math. 54(1) (2009), 1–6. source |
Proceedings, Book Chapters, and Edited-Volume Contributions
Refereed or scholarly contributions appearing in conference proceedings or edited research volumes.
| Year | Area | Citation / Link |
|---|---|---|
| 2017 | Sampling / Book Chapter | V. Oussa, “Regular Sampling on Metabelian Nilpotent Lie Groups: The Multiplicity-Free Case,” in Frames and Other Bases in Abstract and Function Spaces, 377–411, Birkhäuser, 2017. chapter link |
| 2015 | Gabor Theory / Proceedings | V. Oussa, “Decompositions of Rational Gabor Representations,” Contemporary Mathematics 650 (2015), 37–54. arXiv |
| 2015 | Sampling / Conference Proceedings | B. Currey, A. Mayeli, and V. Oussa, “Sampling and Interpolation on Certain Nilpotent Lie Groups,” 2015 International Conference on Sampling Theory and Applications (SampTA) (2015), 73–77. DOI |
| 2014 | Wavelets / Proceedings | A. Mayeli, B. Currey, and V. Oussa, “Decompositions of Generalized Wavelet Representations,” Contemporary Mathematics 626 (2014), 55–65. arXiv |
| 2013 | Group Actions / Proceedings | D. Arnal, B. Dali, B. Currey, and V. Oussa, “Regularity of abelian linear actions,” in Commutative and Noncommutative Harmonic Analysis and Applications, Contemporary Mathematics 603 (2013), 89–109. volume link |
Publicly Posted Preprints and Submitted Manuscripts
This section lists publicly posted preprints and manuscripts with public records or identifiers.
Journal versions already listed above are not duplicated here merely because an earlier preprint also exists.
Journal versions already listed above are not duplicated here merely because an earlier preprint also exists.
| Year | Area | Citation / Link |
|---|---|---|
| 2025 | HRT Conjecture | V. Oussa, “Trichotomy for the HRT Conjecture for mixed integer configuration” (preprint, 2025). arXiv |
| 2025 | Time–Frequency Analysis / Schwartz Functions | V. Oussa, “Translation–Modulation Identities, Ergodic Log-Products and a Conditional Obstruction for Schwartz Functions” (preprint, 2025). record |
| 2025 | Frames on Lie Groups | V. Oussa, Riesz Bases of Translates on Lie Groups (submitted manuscript, December 2025). DOI / public record |
| 2024 | Algorithmic Lie Theory | V. Oussa, Elementary Algorithms for Lie Algebras in Mathematica with Synthetic Data (June 2024). ResearchGate |
| 2023 | HRT Conjecture | V. Oussa, “Zero Set of Zak Transform and the HRT Conjecture” (2023). arXiv |
| — | Algorithmic Lie Theory | V. Oussa, Computing a Lie Algebra from a Generating Set I. ResearchGate |
| — | HRT Conjecture | V. Oussa, New Insights into the HRT Conjecture. PDF |
Doctoral Dissertation
| Year | Title / Institution | Area |
|---|---|---|
| 2012 |
V. Oussa, “Decomposition of a Quasiregular Representation of Exponential Solvable Lie Groups and Admissibility,” Ph.D. Dissertation, Saint Louis University. |
Harmonic analysis on Lie groups; representation theory; admissibility in non-abelian settings. |