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

- (with H. Burgiel) Gabor Orthonormal bases generated by indicator functions of parallelepiped-shaped sets, 2016 (20 pages)

- V. Oussa Frames arising from irreducible solvable actions Part I, 2017 (49 pages)
- (with Brian Sheehan) Dihedral group frames with the Haar property, 2017 (12 pages)

- (with B. Currey and H. Fuehr) A classification of continuous wavelet transforms in dimension three, to appear in Applied and Computational Harmonic Analysis, 2017
- 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)
- V. Oussa Sampling and interpolation on some nilpotent Lie groups, Forum Math. 28 (2016), no. 2, 255–273
- (with D. Arnal and B. Currey) Characterization For
Regularity For a Connected Abelian Action, Monatsh. Math. 180 (2016), no. 1, 1–37

- (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)
- V. Oussa Decomposition of Rational Gabor Representations, Contemporary Mathematics, Contemporary Mathematics 650, 37-54 (2015)
- V. Oussa Dihedral Group Frames which are Maximally Robust to Erasures, Linear and Multilinear Algebra, Volume 63, Issue 12, 2015
- (with B. Currey and A. Mayeli) Decompositions of Generalized Wavelet Representations, Contemporary Mathematics 626, 55-65 (2014)
- 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)
- V. Oussa Computing Vergne Polarizing Subalgebras, Linear and Multilinear Algebra, Volume 63, Issue 3; (2015).
- (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
- (with A. Mayeli) Regular Representations of Time Frequency Groups, Math. Nachr. 287, No. 11-12, 1320-1340 (2014).
- Admissibility For Quasiregular Representations of Exponential Solvable Lie Groups, Colloq. Math, vol. 131, No. 2 (2013)
- (with D. Arnal, B. Currey and B. Dali) Regularity of abelian linear actions, Contemporary Math, American Mathematical Society 2013; 195 pp; Volume: 603
- 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)
- (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)

- Bandlimited Spaces on Some 2-step Nilpotent Lie Groups With One Parseval Frame Generator, Rocky Mountain Journal of Mathematics, Volume 44, Number 4, 2014.
- (with B. Currey) Admissibility for Monomial Representations of Exponential Lie Groups, Journal of Lie Theory 22 (2012), No. 2, 481-487.
- (Dissertation) Decomposition
of a quasiregular representation of exponential solvable Lie groups and
admissibility, Saint Louis University, 2012, 115 pages;
3516239.

- (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.
- (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.