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I am interested in representation theory and harmonic analysis of solvable Lie groups. I am also interested in time-frequency analysis (Gabor Theory), frame, sampling, interpolation, and wavelet theories on non-commutative domains.


Preprints and notes
  1. (with H. Burgiel) Gabor Orthonormal bases generated by indicator functions of parallelepiped-shaped sets, 2016 (20 pages)
  2. V. Oussa Frames arising from irreducible solvable actions Part I, 2017 (49 pages)
  3. (with Brian Sheehan) Dihedral group frames with the Haar property, 2017  (12 pages)
  Publications
  1. (with B. Currey and H. Fuehr) A classification of continuous wavelet transforms in dimension three, to appear in Applied and Computational Harmonic Analysis, 2017
  2. V. Oussa Regular Sampling on Metabelian Nilpotent Lie Groups: The Multiplicity-Free Case, to appear in the book Frames and Other Bases in Abstract and Function Spaces for Applied and Numerical Harmonic Analysis series (ANHA) published by  Birkhauser/Springer in 2017 (Book Chapter)
  3. V. Oussa Sampling and interpolation on some nilpotent Lie groups, Forum Math. 28 (2016), no. 2, 255–273 
  4. (with D. Arnal and B. Currey) Characterization For Regularity For a Connected Abelian Action, Monatsh. Math. 180 (2016), no. 1, 1–37
  5. (with B. Currey and A. Mayeli) Sampling and Interpolation on Certain Nilpotent Lie Groups, SampTA 2015, the 11th International Conference on Sampling Theory and Applications (2015)
  6. V. Oussa Decomposition of Rational Gabor Representations, Contemporary Mathematics, Contemporary Mathematics 650, 37-54 (2015)
  7. V. Oussa Dihedral Group Frames which are Maximally Robust to Erasures Linear and Multilinear Algebra, Volume 63, Issue 12, 2015
  8. (with B. Currey and A. Mayeli) Decompositions of Generalized Wavelet Representations, Contemporary Mathematics 626, 55-65 (2014)
  9. V. Oussa Sinc Type Functions on a Class of Nilpotent Lie Groups, Advances in Pure and Applied Mathematics. Volume 5, Issue 1, Pages 5–19 (2014)
  10.  V. Oussa Computing Vergne Polarizing Subalgebras,  Linear and Multilinear Algebra, Volume 63, Issue 3; (2015).
  11. (with B. Currey and A. Mayeli) Shift-invariant spaces on SI/Z Lie groups Journal of Fourier Analysis and Applications, April 2014, Volume 20, Issue 2, pp 384-400
  12. (with A. Mayeli) Regular Representations of Time Frequency Groups Math. Nachr. 287, No. 11-12, 1320-1340 (2014).
  13.  Admissibility For Quasiregular Representations of Exponential Solvable Lie GroupsColloq. Math, vol. 131, No. 2 (2013)
  14. (with D. Arnal, B. Currey and B. Dali) Regularity of abelian linear actionsContemporary Math, American Mathematical Society 2013; 195 pp; Volume: 603
  15. V. Oussa Shannon-Like Wavelet Frames on a Class of Nilpotent Lie Groups, Int. Jour. of Pure and Applied Mathematics, vol. 84, No. 4 (2013)
  16. (wth D. Ferrone) Linear Independence of a Finite Set of Dilations by a One-Parameter Matrix Lie Group, Int. Jour. of Pure and Applied Mathematics, vol. 84, No. 2 (2013)
  17. Bandlimited Spaces on Some 2-step Nilpotent Lie Groups With One Parseval Frame  Generator, Rocky Mountain Journal of Mathematics, Volume 44, Number 4, 2014.
  18. (with B. Currey) Admissibility for Monomial Representations of Exponential Lie Groups, Journal of Lie Theory 22 (2012), No. 2, 481-487.
  19. (Dissertation) Decomposition of a quasiregular representation of exponential solvable Lie groups and admissibility, Saint Louis University, 2012, 115 pages; 3516239.
  20.  (with U. Ledzewicz and H. Schaettler) Optimal solutions of a model of tumor anti-angiogenesis with a penalty on the cost of treatment, Applicationes Mathematicae, 36 (3), (2009), pp. 295-312.
  21. (with U. Ledzewicz and H. Schaettler) Model for cancer therapy with penalty on the cost of treatment, International Journal of Pure and Applied Mathematics, 54 (1),  (2009),  pp. 1-6.