* Mathematics is the art of giving the same name to different things *

- Henri Poincaré. (click HERE for the full interview)

As a fiction writer, I sign Daniel Zamith-Abreu. My first book, a satyric novel about administrative bureaucracy with the city of Coimbra as scenario,

written in the inspiring cities of Vienna and Novi Sad is available online at FNAC . TlHIS is the link to the Facebook fan-page

I am an Associated Editor of the journal International Journal of Wavelets, Multiresolution and Information Processin

Hyperuniform states of matter: In the eye of a chicken, a new state of matter comes into view.

Scientific Publications of Luís Daniel Abreu


54. Non-iterative phaseless reconstruction from wavelet transform magnitude (Best Paper Award DAFx19)

Proceedings of the DAFx19. Sound examples: http://ltfat.github.io/notes/055/

(with N. Holighaus, G. Koliander and Z. Průša)

53. Filtering the Continuous Wavelet Transform Using Hyperbolic Triangulations

IEEE Proc. SampTA 2019, Bordeaux, France (2019) (with A. Haimi, G. Koliander and J. L. Romero)

52. Deterministic guarantees for L1-reconstruction: a large sieve approach with geometric flexibility

IEEE Proc. SampTA 2019, Bordeaux, France (2019) (with M. Speckbacher)

51. Random Gabor multipliers and compressive sensing

IEEE Proc. SampTA 2019, Bordeaux, France (2019) (with Georg Tauböck, Shristi Rajbamshi and Peter Balazs)

50. Random Gabor multipliers for compressive sensing: a simulation study

Proceedings of the EUSIPCO 2019. (with Georg Tauböck, Shristi Rajbamshi and Peter Balazs).

49. Characterization of Analytic Wavelet Transforms and a New Phaseless Reconstruction Algorithm

IEEE Trans. Signal Proc. 67 (15), 3894-3908, (2019). (with N. Holighaus, G. Koliander and Z. Prusa)

48. Uniform convergence of basic Fourier-Bessel series on a q-linear grid

The Ramanujan Journal, 49 (2), 421-449, (2019). (with R. Alvarez-Nodarse and J. L. Cardoso)

47. Harmonic analysis in phase space and finite Weyl- Heisenberg ensembles

J. Statistical Physics, 174 (5), 1104-1136, (2019). (with K. Gröchenig and J. L. Romero)


46 (with Michael Speckbacher). Donoho-Logan large sieve principles for modulation and polyanalytic Fock space

45. Filtering with Wavelet Zeros and Gaussian Analytic Functions

undergoing an extended revision (with A. Haimi, G. Koliander and J. L. Romero)


44. Sharp rates of convergence for accumulated spectrograms

Inverse Problems, 33 (11), 115008 (2017). (with J. M. Pereira and J. L. Romero)

43. MSE estimates for multitaper spectral estimation and off-grid compressive sensing

IEEE Trans. Information Theory, 63 (12), 7770-7776 (2017). (with J. L. Romero)

42. The Weyl-Heisenberg ensembles: hyperuniformity and higher Landau levels,

J. Statistical Mechanics: Theor. Exper. 4, 043103 (2017). (with J. L. Romero, J.M. Pereira and S. Torquato)

41. A planar large sieve and sparsity of time-frequency representations

IEEE Proc. SampTA 2017, Tallinn, Estonia, 283-287 (2017). (with M. Speckbacher)

40. The Weyl-Heisenberg ensemble: statistical mechanics meet time-frequency analysis

IEEE Proc. SampTA 2017, Tallinn, Estonia, 199-202 (2017). (with J. L. Romero, J. M. Pereira and S. Torquato)

39. Multitaper spectral estimation and off-grid compressive sensing: MSE estimates

IEEE Proc. SampTA 2017. Tallinn, Estonia, 188-191 (2017). (with J. L. Romero)

38. Superframes and polyanalytic wavelets,

J. Fourier Anal. Appl., 23 (2017) 1-20.

37. The average singular value of a complex random matrix decreases with dimension, arXiv second preliminar version (2017).


36. On accumulated spectrograms,

Trans. Amer. Math. Soc., 368, (2016), 3629-3649. (with K. Gröchenig and J. L. Romero)

35. Discrete coherent states for higher Landau levels (open access HERE ).

Annals of Physics, 363 (2015) 337-353. ( with P. Balazs, M. de Gosson and Z. Mouayn).

Press release from the Austrian Academy of Sciences: MUSICAL ELECTRONS (in German) ).

34. The bias-variance trade-off in Thomson´s multitaper estimator ,

Technical Report (2015). (with J. L. Romero)

33. Pseudo prolate spheroidal functions,

IEEE Proc. SampTA 2015, 603-607 (2015). (DOI 10.1109/SAMPTA.2015.7148962 ). (with J. M. Pereira)

32. Measures of localization and quantitative Nyquist densities,

Appl. Comp. Harm. Anal., 38 (2015), 524-534. (with J. M. Pereira)

31. On Toeplitz operators and localization operators,

Proc. Amer. Math. Soc. 143 (2015), 4317-4323. (with N. Faustino)


30. L. D. Abreu, Special frames, Proceedings of the SampTA 2013. Bremen, Germany, 176-177, Eurasip, (2014)

29. L. D. Abreu, J. E. Gilbert, Wavelet-type frames for the interval, Expo. Math., 32 (2014) 274 – 283.

28. L. D. Abreu, H. G. Feichtinger, Function spaces of polyanalytic functions, Harmonic and Complex Analysis and its Applications, Springer, pp. 1-38 (2014).

27. L. D. Abreu, O. Ciaurri, J. L. Varona, The spectrum of the right inverse of the Dunkl operator, Rev. Mat. Complutense , 26, (2013), 471-483.

26. L. D. Abreu, O. Ciaurri and J. L. Varona, A q-linear analogue of the plane wave expansion, Adv. Appl. Math, 50, No. 3, 415-428 (2013).

25. L. D. Abreu, A. S. Bandeira, Landau´s necessary density conditions for the Hankel transform , J. Funct. Anal. , 162 (2012) 1845-1866.

24. L. D. Abreu, M. Dörfler, An inverse problem for localization operators , Inverse Problems, (2012) 28, 115001, 16 pp.

23. L. D. Abreu, K. Gröchenig, Banach Gabor frames with Hermite functions: polyanalytic spaces from the Heisenberg group, Appl. Anal., 91 (2012), 1981-1997.

22. L. D. Abreu, Super-wavelets versus poly-Bergman spaces, Int. Eq. Oper. Theory, 73 (2012) 177–193.

21. L. D. Abreu, O. Ciaurri and J. L. Varona, Bilinear biorthogonal expansions and the Dunkl kernel on the real line , Expo. Math., 30 (2012), 32-48.

20. M. de Gosson, L. D. Abreu, Weak values and Born-Jordan quantization, AIP Conf. Proc. 1508, pp. (2012) 156-161.

19. L. D. Abreu, Gabor frames, displaced states and the Landau levels: a tour in polyanalytic Fock spaces, “Proceedings 8th ISAAC Congress, Vol. 1, (2012) 197-207.

18. L. D. Abreu, O. Ciaurri, J. L. Varona, Bilinear biorthogonal expansions and the Dunkl kernel on the real line, Expo. Math., 30 (2012), 32-48.

17. L. D. Abreu, Wavelet frames with Laguerre functions, C. R. Math. Acad. Sci. Paris, 349 (2011), 255-258.

16. L. D. Abreu, Sampling and interpolation in Bargmann-Fock spaces of polyanalytic functions, Appl. Comp. Harm. Anal., 29 (2010), 287-302.

15. L. D. Abreu, F. Bouzeffour, A Paley-Wiener theorem for the Askey-Wilson function transform, Proc. Amer. Math. Soc. 138, (2010) 2853-2862.

14. L. D. Abreu, On the structure of Gabor and super Gabor spaces, Monatsh. Math., 161 (2010), no. 3, 237-253.


Old Publications (before 2010):

(13) The reproducing kernel structure arising from a combination of continuous and discrete orthogonal polynomials into Fourier systems.

Constr. Approx. 28 (2008), no. 2, 219-235.

(12) Hardy-type theorem for orthogonal functions with respect to their zeros. The Jacobi weight case. (joint with F. Marcellan e S. B. Yakubovich),

J. Math. Anal. Appl., 341 (2008), no. 2, 803-812.

(11) Remarks on isometric mappings between the Hardy-Szego and Bergman-Selberg spaces: wavelet transforms and Laguerre functions,

Integral Transforms Spec. Funct. 19 (2008), no. 7, 463-470; 

(10) Real Paley-Wiener theorems for the Koornwinder-Swarttouw q-Hankel transform.

J. Math. Anal. Appl., 334, no. 1, 223-231 (2007).

(9) Completeness, special functions, and uncertainty principles over q-linear grids.

J. Phys. A: Math. and Gen., 39 14567-14580 (2006).

(8) Functions q-orthogonal with respect to their own zeros.

Proc. Amer. Math. Soc. 134 , 2695-2701, (2006).

(7) A q-analogue of an inequality due to Konrad Knopp.

J. Ineq. Pure Appl. Math., 7, (3) art. 110, (2006).

(6) Sampling theory associated with q-difference equations of the Sturm-Liouville type.

J. Phys. A: Math. and Gen. 38, no. 48, 10311—10319, (2005).

(5) A q-sampling theorem related to the q-Hankel transform.

Proc. Amer. Math. Soc. 133, 1197-1203, (2005).

(4) Complete sets of q-Bessel functions, (joint with J. Bustoz).

in "Theory and Applications of Special Functions. A volume dedicated to Mizan Rahman", (eds. M. E. H. Ismail and E. Koelink),

Dev. in Math., Springer, New York, (2005).

(3) Connecting Basic Bessel Functions.

in: The J. A. Sampaio Martins anniversary volume, pp. 13-20, Textos Mat. Sér. B 34, DMUC, (2004).

(2) The roots of the third Jackson q-Bessel function, (joint with J. Bustoz e J. L. Cardoso).

Int. J. Math. Math. Sci. 67, (2003), 4241-4248.

(1) Turán inequalities for symmetric Askey-Wilson polynomials, (joint with J. Bustoz).

Rocky Mountain. J. Math. 30, (2000), no. 2, 401-409.