Publications

Books & Edited Volumes

  1. Modulation Spaces: With Applications to Pseudodifferential Operators and Nonlinear Schrodinger Equations, A. Benyi and K. A. Okoudjou, Applied and Numerical Harmonic Analysis, Birkhauser, Bassel, (2020).
  2. Sampling: Theory and Applications, Eds S. D. Casey, K. A. Okoudjou, M. Robinson, and B. Sadler, Applied and Numerical Harmonic Analysis, Birkhauser, Basel, 2020.
  3. Recent Advances in Mathematics and Technology: Proceedings of the First International Conference on Technology, Engineering, and Mathematics, Kenitra, Morocco, March 26-27, 2018, Eds S. Dos Santos, M. Maslouhi, and K. A. Okoudjou, Applied and Numerical Harmonic Analysis, Birkhauser, Bassel, (2020).
  4. Excursions in Harmonic Analysis, Vol. V; Eds R. Balan, J. J. Benedetto, W. Czaja, M. Dellatorre, and K. A. Okoudjou Birkhauser/Springer, New York, 2017 Vol V
  5. Finite Frame Theory: A Complete Introduction to Overcompleteness, Ed K. A. Okoudjou, Proceedings of Symposia in Applied Mathematics, Vol. 73, AMS (2016).
  6. Excursions in Harmonic Analysis, Vol. IV; Eds R. Balan, M. Begue, J. J. Benedetto, W. Czaja, K. A. Okoudjou; Birkhauser, New York, 2015 Vol IV
  7. Excursions in Harmonic Analysis, Vol. III; Eds R. Balan, M. Begue, J. J. Benedetto, W. Czaja, K. A. Okoudjou; Birkhauser, New York, 2015 Vol III
  8. Excursions in Harmonic Analysis, Vol. II; Eds T. Andrews, R. Balan, J. J. Benedetto, W. Czaja, K. A. Okoudjou; Birkhauser, New York, 2013 Vol II
  9. Excursions in Harmonic Analysis, Vol. I; Eds T. Andrews, R. Balan, J. J. Benedetto, W. Czaja, K. A. Okoudjou; Birkhauser, New York, 2013 Vol I

Refeered Journal Publications

Time-Frequency Analysis

  1. An algebraic perspective on multivariate tight wavelet frames with rational masks, (with Y. Hur and Z. Lubberts), arXiv:1902.07800, submitted, March 2019.
  2. Bimodal Wilson systems in L^2(\mathbb{R}), (with D. G. Bhimani), arXiv:1812.08020, submitted, December 2018.
  3. On the frame set for the 2-spline, (with A. G. D. Atindehou, and Y. B. Kouagou), arXiv:1806.05614, submitted, June 2018.
  4. Finding duality and Riesz bases of exponentials on multi-tiles,(with C. Frederick), arXiv:1910.09257, Appl. Comput. Harmon. Anal., to appear.
  5. The Hartree-Fock equations in modulation spaces, (with D. Bhimani and M. Grillakis), arXiv:1908.05862, Comm. Partial Differential Equations 45 (2020), no. 9, 1088–1117.
  6. Frame sets for a class of compactly supported continuous functions, (with A. G. D. Atindehou and Y. B. Kouagou) arXiv:1804.02450, Asian-Eur. J. Math., 13 (2020), no. 5.
  7. Extension and restriction principles for the HRT conjecture, arXiv:1701.08129, J. Fourier Anal. Appl., 25 (2019), no. 4, 1874-1901.
  8. An invitation to Gabor analysis, arXiv:1812.08647, Notices Amer. Math. Soc., 66 (2019), no. 6, 808-819.
  9. On a Feichtinger problem, (with R. Balan, andA. Poria) arXiv:1705.06392, Operators and Matrices 12 (2018), no. 3, 881 – 891.
  10. On Wilson bases in L^2(\mathbb{R}^d), (with M. Bownik, M. S. Jakobsen, and J. Lemvig) arXiv:1703.08600, SIAM J. Math. Anal. 49 (2017), no. 5, 3999-4023.
  11. Boundedness of multilinear pseudo-differential operators on modulation spaces, (with S. Molahajloo, and G. E. Pfander), arXiv:1502.03317, J. Fourier Anal. Appl., 22 (2016), no. 6, 1381-1415.
  12. Scaling Laplacian pyramids, (with Y. Hur), arXiv:1409.6938, SIAM J. Matrix Anal. Appl., 36(1) (2015), 348-365.
  13. Multi-window Gabor frames in amalgam spaces (with R. Balan, J. Christensen, I. Krishtal and J.L. Romero), arXiv:1108.6108 Math. Res. Lett., 21(2014), no.1, 1-15.
  14. Dilation properties for weighted modulation spaces (with Elena Cordero), arXiv:1008.0266 J. Funct. Spaces Appl., Vol. 2012, Article ID 145491, 29 pages; doi:10.1155/2012/145491.
  15. Local well-posedness of nonlinear dispersive equations on modulation spaces (with A. Benyi), arXiv:0704.0833, Bulletin of the London Mathematical Society, 41 (2009) no. 3, 549-558.
  16. A Beurling-Helson type theorem for modulation spaces, arXiv:0801.1338, J. Funct. Spaces Appl., 7 (2009), no. 1, 33-41.
  17. Invertibility of the Gabor frame operator on the Wiener amalgam space (with I. Krishtal), arXiv:0705.1335, J. Approximation Theory, 153 (2008), no. 2, 212-224.
  18. Time-frequency estimates for pseudodifferential operators (with A. Benyi), Contemporary Math., AMS, Vol. 428 (2007), 13-22.
  19. Unimodular Fourier multipliers on modulation spaces, (with A. Benyi, K. Groechenig and L. Rogers), arXiv:math/0609097 , J. Funct. Anal. 246 (2007), no. 2, 366-384.
  20. Multilinear localization operators (with E. Cordero), J. Math. Anal. Appl., 325 (2007), no. 2, 1103–1116.
  21. Modulation spaces estimates for multilinear pseudodifferential operators (with A. Benyi), Studia Math., 172 (2006), no. 2, 169-180.
  22. Modulation spaces and a class of bounded multilinear pseudodifferential operators (with A. Benyi, K. Groechenig and C. Heil), J. Operator Theory, 54 (2005), no. 2, 389-401.
  23. A class of Fourier multipliers for modulation spaces, (with A. Benyi, L. Grafakos and K. Groechenig), Appl. Comput. Harmon. Anal. 19 (2005), no 1, 131-139.
  24. Bilinear pseudodifferential operators on modulation spaces (with A. Benyi), J. Fourier Anal. Appl. 10 (2004), no 3, 301-313. .
  25. Embeddings of some classical Banach spaces into the modulation spaces, Proc. Amer. Math. Soc. 132 (2004), no. 6, 1639-1647.
  26. Gabor analysis in weighted amalgam spaces (with K. Groechenig and C. Heil), Sampl. Theory Image Signal Process. 1 (2003), no. 3, 225-260.

Frame theory

  1. Gradient Flows for Frame Potentials on the Wasserstein Space, (with C. Wickman), arXiv:1808.09319, submitted, August 2018.
  2. Universal optimal configurations for the p-frame potentials, (with X. Chen, V. Gonzales, E. Goodman, and S. Kang), arXiv:1902.03505, Adv. Comput. Math., 46 (2020), 4.
    Numerical data about this manuscript can be found here.
  3. Optimal properties of the canonical tight probabilistic frame, (with D. Cheng) arXiv:1705.03437, Numer. Funct. Anal. Optim., 40 (2019), no. 2, 216-240.
  4. Equiangular quantum key distribution in more than two dimensions, (with R. Balu, P. J. Koprowski, J. S. Park, and G. Siopsis), arXiv:1810.05161, J. Phys. A: Math. Theor., 52 (2019), no. 075202.
  5. Duality and geodesics for probabilistic frames, (with C. Wickman), arXiv:1609.05998, Linear Algebra and its Applications, 532 (2017), 198 – 221.
  6. Measures of scalability (with X. Chen, G. Kutyniok, F. Philipp, and R. Wang), arXiv:1406.2137, IEEE Trans. Inf. Theory, 61 (2015), no. 8, 4410-4423.
  7. Finite two-distance tight frames, (with A. Barg, A. Glazyrin, and W.-H. Yu), arXiv:1402.3521, Linear Algebra and its Applications, 475 (2015), 163-175.
  8. Scalable frames and convex geometry (with G. Kutyniok and F. Philipp), arXiv:1310.8107 , Contemp. Math., Vol. 626 (2014), 19-32.
  9. Prime tight frames (with J. Lemvig, and C. Miller), arXiv:1202.6350 Adv. Comput. Math., 40 (2014), no. 2, 315-334.
  10. Scalable frames (with Gitta Kutyniok, Friedrich Philipp and Kaitlyn E. Tuley), arXiv:1204.1880, Linear Algebra and its Applications 438 (2013) 2225–2238.
  11. Minimization of the Probabilistic p-frame Potential (with Martin Ehler), arXiv:1101.0140, J. Statist. Plann. Inference, 142 (2012), no. 3, 645-659.
  12. Frame potential and finite abelian groups, (with B. D. Johnson), arXiv:0801.3813 , Contemporary Math., AMS, Vol. 464 (2008), 137-148.
  13. Convolutional frames and the frame potential, (with M. Fickus, B.D. Johnson and K. Kornelson), Appl. Comput. Harmon. Anal. 19 (2005), no 1, 77-91.

Analysis on Fractals and Graphs

  1. Sobolev Orthogonal Polynomials on the Sierpinski gasket, (with Q. Jiang, T. Lan, R. S. Strichartz, S. Sule, S. Venkat, and X. Wang), arXiv:2010.00107 , submitted, October 2020.
  2. The strong maximum principle for Schrodinger operators on fractals, (with M. Ionescu and L. Rogers), arXiv:1902.05584, Demonstr. Math., 52 (2019), 404-409.
  3. Invertibility of graph translation and support of Laplacian Fiedler vectors, (with M. Begue) arXiv:1703.05867, Contemp. Math., 706 (2018), 153-174.
  4. Some spectral properties of pseudo-differential operators on the Sierpinski gasket, (with M. Ionescu, and L. G. Rogers), arXiv:1406.5165, Proc. Amer. Math. Soc., 145 (2017), no. 5, 2183-2198.
  5. Orthogonal polynomials on the Sierpinski gasket (with R. S. Strichartz and E. K. Tuley), arXiv:1110.1554, Constr. Approx., 37 (2013), no. 3, 311-340.
  6. Szego limit theorems on the Sierpinski gasket (with L. G. Rogers and R. S. Strichartz), arXiv:0810.2315 J. Fourier Anal. Appl., 16 (2010), no. 3, 434–447.
  7. Generalized eigenfunctions and a Borel theorem on the Sierpinski gasket (with L. G. Rogers and R. S. Strichartz), Canadian Mathematical Bulletin, 52 (2009), no. 1, 105-116.
  8. An uncertainty principle for graphs, fractals and manifolds (with L. Saloff-Coste and A. Teplyaev), arXiv:math/0701207, Trans. Amer. Math. Soc., 360 (2008), no. 7, 3857-3873.
  9. Asymptotics of eigenvalue clusters for Schrodinger operators on the Sierpinski gasket (with R. S. Strichartz), Proc. Amer. Math. Soc. 135 (2007), no. 8, 2453-2459.
  10. Weak uncertainty principles on fractals (with R. S. Strichartz), J. Fourier Anal. Appl. 11, no 3, 315-331.

Math Education

  1. Active learning in an undergraduate precalculus course: Insights from a course redesign (with S. Gruber, R. Rosca, D. Chazan, E. Fleming, S. Balady, and C. Van Netta), PRIMUS, May 2020, DOI: 10.1080/10511970.2020.1772920

Book Chapters

  1. Optimal l-one Rank One Matrix Decompositions, (with R. Balan, M. Rawson, Y. Wang, and R. Zhang), arXiv:2002.00879, submitted, January 2020.
  2. Optimization methods for frame conditioning and application to graph Laplacian scaling, (with R. Balan, M. Begue, and C. Clark) arXiv:1609.02233, in “Frames and other bases in abstract and function spaces,” Lecture Notes ANHA Series, I. Pesenson and all Eds., 27 – 45, Appl. Numer. Harmon. Anal., Birkhauser/Springer, Cham, 2017.
  3. Preconditioning techniques in frame theory and probabilistic frames, arXiv:1504.02023 in “Finite Frame Theory: A Complete Introduction to Overcompleteness”, Ed. K. A. Okoudjou, Proceedings of Symposia in Applied Mathematics, Vol. 73, 105-142, AMS (2016). (Notes from my lecture at the AMS 2015 Short Course on Finite Frame Theory: A Complete Introduction to Overcompleteness).
  4. Probabilistic frames: An overview (with Martin Ehler), arXiv:1108.2169, in “Finite Frames: Theory and Applications”, Applied and Numerical Harmonic Analysis, P. G. Casazza and G. Kutyniok (Eds), 415-436, Birkhauser (2013).

Refeered Conference Proceedings

  1. Optimal frame conditioners, (with C. A. Clark), Proceedings SAMPTA 2015, pp. 148-152, doi: 10.1109/SAMPTA.2015.7148869.
  2. Preconditioning of frames, (with G. Kutyniok and F. Philipp), Proc. SPIE 8858, Wavelets and Sparsity XV, 88580G (September 26, 2013).
  3. Perfect preconditioning of frames by a diagonal operator, (with G. Kutyniok and F. Philipp), Proceedings of the 10th International Conference on Sampling Theory and Applications pp. 85-88.
  4. Concatenating codes for improved ambiguity behavior, (with J. J. Benedetto, A. Bourouihiya, I. Konstantinidis), Proceedings ICEAA ’07.