# Publications


Back to the homepage of Azita Mayeli


Peer-Reviewed Publications since 2006

1. Identification of Besov spaces via Littlewood-Paley-Stein g-type function, accepted for publication in Proceeding of American Mathematical Society.
2. (with D.Barbier and E. Hernandez) Lattice sub-tilings and frames in LCA groups, accepted for publication in Comptes rendus Mathematique.
3. (with Alex Iosevich and Jonathan Pakianathan) The Fuglede Conjecture holds in ${\Bbb Z}_p \times {\Bbb Z}_p$, accepted for publication in Analysis and PDE.
4. A unified Littlewood-Paley decomposition of abstract Besov spaces; Proc. Amer. Math. Soc., Proc. Amer. Math. Soc. 144 (2016), 1021--1028.
5. (with Bradley Currey and  Vignon Oussa), Sampling and Interpolation on Certain Nilpotent Lie Groups, to appear in IEEE Sampling, 2015.
6. (with A. Iosevich), Exponential bases, Paley-Wiener spaces, and applications; Journal of Functional Analysis, Volume 268, Issue 2, 15 January 2015, Pages 363--375.
7. (with B. Currey and V. Oussa), Decompositions of Generalized Wavelet Representations; Contemporary Mathematics 626, 55-65 (2014)
8. ﻿(with B. Currey and V. Oussa), Characterization of shift-invariant spaces on a class of nilpotent Lie groups with applications; Journal of Fourier Analysis and Applications, April 2014, Volume 20, Issue 2, pp 384-400.
9. (with D.Barbier and E. Hernandez) Bracket map for Heisenberg group and the characterization of cyclic subspace; Applied and Computational Harmonic Analysis, Volume 37, Issue 2, September 2014, Pages 218--234.
10. ﻿(with V. Oussa) Regular Representations of Time-Frequency Groups;  Mathematische Nachrichten, Volume 287, Issue 11-12, pages 1320–1340, 2014.
11. (with M. Razani), Multiplexing and demultiplexing Frame Pairs; to appear in Contemprory Mathematics, Nov. 2013.
12. (with B. Currey), The orthonormal dilation property for abstract Parseval wavelet frames; Canadian Mathematical Bulletin, 56(2013), 729-736.
13. (With J. Christensen, G. Olafsson) Coorbit description and atomic decomposition of Besov spaces; Numerical Functional Analysis and Optimization, pages 847-871, 24 pages, (2012).
14. (with H. Führ), Homogeneous Besov spaces on stratified Lie groups and their wavelet chracterization;  The Journal of Function Spaces and Applications, Volume 2012, Article ID 523586, (2012), 41 pages.
15. (with B. Currey), A density condition for interpolation on the Heisenberg group; (arXiv), Rocky Mountain Journal of Mathemathics, Volume 42, Number 4 (2012), pages 1135-1151, 17 pages,
16. (with S.Scodeller, O.Rudjord, F.K.Hansen, D.Marinucci, D. Geller) Introducing Mexican needlets for CMB analysis: Issues for practical applications and comparison with standard needlets, The Astrophysical Journal, Vol. 733, No. 2, (2011).
17. (with B. Currey), Gabor fields and wavelet sets for the Heisenberg group; Monatsh. Math. (2011), 162:119-142.
18. (with D. Geller), Nearly tight frames for spin wavelets on the sphere; Sampl. Theory Signal Image Process. 9 (2010),  25-57.
19. Asymptotic uncorrelation for generalized mexican needlets;J. Math. Anal. Appl.  (2010), Pages 336-34.
20. (with D. Geller), Besov spaces and frames on compact manifolds; (arXiv) Indiana Univ. Math. J.  58 (2009),  2003-2042.
21. (with D. Geller), Nearly tight frames and space-frequency analysis on compact manifolds;Math. Z. 236 (2009), no. 2, 235-264
22. (with D. Geller), Continuous wavelets on compact manifolds; Math. Z. 262 (2009), no. 4, 895--927
23. Shannon multiresolution analysis on the Heisenberg group; J. Math. Anal. Appl. 348 (2), 671-684, (2008)
24. (with D. Geller ), Continuous wavelets and frames on stratified Lie groups I.; J. Fourier Anal. Appl. 12 (5), 543-579, (2006)
25. Continuous and Discrete Wavelet Transformations on the Heisenberg Group; (Ph.D thesis in English) accepted by Technische Universität München, Germany in April 2006.
###### Preprints/papers submitted
1. (with D.Barbier and E. Hernandez) Calder\'on-type inequalities for affine frames, submitted.
2. Riesz wavelets, tiling and spectral sets in LCA groups, submitted.
3. (with Alex Iosevich and Chun-Kit Lai) Tight wavelet frame sets on finite vector spaces, submitted.
4. (with Alex Iosevich, Allen Liu and Jonathan Pakianathan) On an analog of Nyquist-Shannon type theorems in vector spaces over finite fields, submitted

5. (with V. Oussa) Sampling pairs for a class of nilpotent Lie groups, preprint.
6. (with D.Barbier and E. Hernandez) Tiling by lattices for locally compact abelian groups, preprint, http://arxiv.org/pdf/1508.04208v1.pdf
7. Azita Mayeli, Paley-Wiener description of K-spherical Besov spaces on the Heisenberg group, preprint, http://arxiv.org/pdf/1111.4573v1.pdf
8. Azita Mayeli, Mexican wavelet on the Heisenberg group, 2008.  http://arxiv.org/abs/0705.3364
###### Book chapter.
1. Azita Mayeli and Daryl Geller, Wavelets on Manifolds and Statistical Applications to Cosmology; title of the book: Wavelets and Multiscale Analysis, Theory and Applications,published by Birkhaeuser, 2011.
##### Books and Conference Proceedings
1. Alex Iosevich, Azita Mayeli, Steven Senger, Fourier bases: an elementary viewpoint on a variety of applications, submitted to AMS Student Mathematical Library.
2. Jens Christensen, Susanna Dann, Azita Mayeli, Gestur Olafsson, Harmonic Analysis and its Applications, AMS Contemporary Mathematics, Volume: 650, 2015, 209 pp.
3. Azita Mayeli, Alex Iosevich, Palle T. Jorgensen, and Gestur Olafsson, Commutative and Noncommutative Harmonic Analysis and Applications, AMS, Contemporary Mathematics, Vol. 603, 2013. ISBN-10: 0-8218-9493-5 Link: http://www.ams.org/bookstore
4. Azita Mayeli, Continuous and Discrete Wavelet Transformations on the Heisenberg Group; published by Technische Universitaet Muenchen Press (Technical Univesrity of Munich), Germany,  2006.
##### Some notes for my students

last updated: August 25, 2015

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