**Refeered Journal Publications**

- The strong maximum principle for Schrodinger operators on fractals, (with M. Ionescu and L. Rogers), submitted, February 2019.
- Universal optimal configurations for the p-frame potentials, (with X. Chen, V. Gonzales, E. Goodman, and S. Kang), arXiv:1902.03505, submitted, February 2019.
- An invitation to Gabor analysis, arXiv:1812.08647, submitted, December 2018.
- Bimodal Wilson systems in L_2(R), (with D. G. Bhimani), arXiv:1812.08020, submitted, December 2018.
- Gradient Flows for Frame Potentials on the Wasserstein Space, (with C. Wickman), arXiv:1808.09319, submitted, August 2018.
- On the frame set for the 2-spline, (with A. G. D. Atindehou, and Y. B. Kouagou), arXiv:1806.05614, submitted, June 2018.
- 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.,**to appear. - Extension and restriction principles for the HRT conjecture,
arXiv:1701.08129,
**J. Fourier Anal. Appl.,**to appear. - Optimal properties of the canonical tight probabilistic frame, (with D. Cheng)
arXiv:1705.03437,
**Numer. Funct. Anal. Optim.,**to appear. - 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.** - On a Feichtinger problem, (with R. Balan, andA. Poria) arXiv:1705.06392,
**Operators and Matrices 12 (2018), no. 3, 881 - 891.** - Invertibility of graph translation and support of Laplacian Fiedler vectors, (with M. Begue)
arXiv:1703.05867,
**Contemp. Math., 706 (2018), 153-174.** - On Wilson bases in L2(R^d), (with M. Bownik, M. S. Jakobsen, and J. Lemvig)
arXiv:1703.08600,
**SIAM J. Math. Anal. 49 (2017), no. 5, 3999-4023.** - Duality and geodesics for probabilistic frames, (with C. Wickman),
arXiv:1609.05998,
**Linear Algebra and its Applications, 532 (2017), 198 - 221.** - Some spectral properties of pseudo-differential
operators on the Sierpinski gasket, (with M. Ionescu, and L. G.
Rogers), [pdf],
**Proc. Amer. Math. Soc., 145 (2017), no. 5, 2183-2198.** - Boundedness of multilinear pseudo-differential operators on modulation spaces,
(with S. Molahajloo, and G. E. Pfander),
[pdf],
**J. Fourier Anal. Appl., 22 (2016), no. 6, 1381-1415.** - Measures of scalability (with X. Chen, G. Kutyniok,
F. Philipp, and R. Wang), [pdf],
**IEEE Trans. Inf. Theory, 61 (2015), no. 8, 4410-4423.** - Finite two-distance tight frames, (with A. Barg, A. Glazyrin, and W.-H. Yu),
[pdf],
**Linear Algebra and its Applications, 475 (2015), 163-175.** - Scaling Laplacian pyramids, (with Y. Hur), [pdf],
**SIAM J. Matrix Anal. Appl., 36(1) (2015), 348-365.** - Scalable frames and convex geometry (with G. Kutyniok
and F. Philipp), [pdf],
**Contemp. Math., Vol. 626 (2014), 19-32.** - Multi-window Gabor frames in amalgam spaces (with R.
Balan, J.
Christensen, I. Krishtal and J.L. Romero), [pdf]
[ps]
**Math. Res. Lett., 21(2014), no.1, 1-15.** - Prime tight frames (with J. Lemvig, and C. Miller), [pdf]
**Adv. Comput. Math., 40 (2014), no. 2, 315-334.** - Orthogonal polynomials on the Sierpinski gasket (with
R. S. Strichartz and E. K. Tuley), [pdf]
[ps] ,
**Constr. Approx., 37 (2013), no. 3, 311-340.** - Scalable frames (with Gitta Kutyniok, Friedrich
Philipp and Kaitlyn E. Tuley),
[pdf], [ps],
**Linear Algebra and its Applications 438 (2013) 2225–2238.** - Minimization of the Probabilistic p-frame Potential
(with Martin Ehler), [pdf] [ps],
**J. Statist. Plann. Inference, 142 (2012), no. 3, 645-659.** - Dilation properties for weighted modulation spaces
(with Elena Cordero), [pdf] [ps],
**J. Funct. Spaces Appl., Vol. 2012, Article ID 145491, 29 pages; doi:10.1155/2012/145491.** - Szego limit theorems on the Sierpinski gasket (with
L. G. Rogers and R. S. Strichartz), [pdf]
[ps],
**J. Fourier Anal. Appl., 16 (2010), no. 3, 434--447.** - Local well-posedness of nonlinear dispersive
equations on modulation spaces (with A. Benyi), [pdf]
[ps],
**Bulletin of the London Mathematical Society, 41 (2009) no. 3, 549-558.** - A Beurling-Helson type theorem for modulation spaces,
[pdf], [ps],
**J. Funct. Spaces Appl., 7 (2009), no. 1, 33-41.** - Generalized eigenfunctions and a Borel theorem on the
Sierpinski gasket (with L. G. Rogers and R. S. Strichartz), [pdf],
**Canadian Mathematical Bulletin, 52 (2009), no. 1, 105-116.** - Invertibility of the Gabor frame operator on the
Wiener amalgam space (with I. Krishtal), [pdf],
[ps],
**J. Approximation Theory, 153 (2008), no. 2, 212-224.** - Frame potential and finite abelian groups, (with B.
D. Johnson), [pdf] ; [ps],
**Contemporary Math., AMS, Vol. 464 (2008), 137-148.** - An uncertainty principle for graphs, fractals and
manifolds (with L. Saloff-Coste and A. Teplyaev), [pdf], [ps],
**Trans. Amer. Math. Soc., 360 (2008), no. 7, 3857-3873.**. - Time-frequency estimates for pseudodifferential
operators (with A. Benyi), [pdf]
,
**Contemporary Math., AMS, Vol. 428 (2007), 13-22.** - Asymptotics of eigenvalue clusters for Schrodinger
operators on the Sierpinski gasket (with R. S. Strichartz), [pdf], [ps] ,
**Proc. Amer. Math. Soc. 135 (2007), no. 8, 2453-2459.** - Unimodular Fourier multipliers on modulation spaces,
(with A. Benyi, K. Groechenig and L. Rogers),
[pdf] , [ps] ,
**J. Funct. Anal. 246 (2007), no. 2, 366-384.** - Multilinear localization operators (with E. Cordero), [pdf], [ps],
**J. Math. Anal. Appl., 325 (2007), no. 2, 1103--1116.** - Modulation spaces estimates for multilinear
pseudodifferential operators (with A. Benyi), [pdf];
[ps],
**Studia Math., 172 (2006), no. 2, 169-180.** - Modulation spaces and a class of bounded multilinear
pseudodifferential operators (with A. Benyi, K. Groechenig and C.
Heil), [pdf]; [ps],
**J. Operator Theory, 54 (2005), no. 2, 389-401.** - A class of Fourier multipliers for modulation spaces,
(with A. Benyi, L. Grafakos and K. Groechenig), [ps],;
[pdf],
**Appl. Comput. Harmon. Anal. 19 (2005), no 1, 131-139.** - Convolutional frames and the frame potential, (with M.
Fickus, B.D. Johnson and K. Kornelson),
[pdf]; [ps],
**Appl. Comput. Harmon. Anal. 19 (2005), no 1, 77-91.** - Weak uncertainty principles on fractals (with R. S.
Strichartz), [pdf]; [ps],
**J. Fourier Anal. Appl. 11, no 3, 315-331.** - Bilinear pseudodifferential operators on modulation
spaces (with A. Benyi), [pdf],
**J. Fourier Anal. Appl. 10 (2004), no 3, 301-313.**. - Embeddings of some classical Banach spaces into the
modulation spaces, [pdf],
**Proc. Amer. Math. Soc. 132 (2004), no. 6, 1639-1647.** - Gabor analysis in weighted amalgam spaces (with K.
Groechenig and C. Heil), [pdf],
**Sampl. Theory Image Signal Process. 1 (2003), no. 3, 225-260.**

**Book Chapters**

- 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.** - Preconditioning techniques in frame theory and probabilistic frames,
[pdf] 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). - Probabilistic frames: An overview (with Martin
Ehler), [pdf] [ps], 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**

- Optimal frame conditioners, (with C. A. Clark), [pdf], Proceedings SAMPTA 2015, to appear.
- Preconditioning of frames, (with G. Kutyniok and F. Philipp), [pdf], Proc. SPIE 8858, Wavelets and Sparsity XV, 88580G (September 26, 2013).
- Perfect preconditioning of frames by a diagonal operator, (with G. Kutyniok and F. Philipp), [pdf] Proceedings of the 10th International Conference on Sampling Theory and Applications pp. 85-88.
- Concatenating codes for improved ambiguity behavior, (with J. J. Benedetto, A. Bourouihiya, I. Konstantinidis), [pdf] Proceedings ICEAA '07.

**Books**

- Finite Frame Theory: A Complete Introduction to Overcompleteness, Ed K. A. Okoudjou, Proceedings of Symposia in Applied Mathematics, Vol. 73, AMS (2016) overcompletness
- 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
- 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
- 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
- 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

**Other Publications**

- Characterization of function spaces and boundedness properties of bilinear pseudodifferential operators through Gabor frames, Ph.D. thesis , August 2003, Georgia Institute of Technology.

*Last modified: February 2019*