Publications

Research publications

* On approximation spaces and greedy type bases.

Berná, P.M., Chu, H.V., Hernández,

Preprint, March 2023: https://arxiv.org/abs/2207.02554

* Learning optimal smooth invariant subspaces for data approximation.

Barbieri D., Cabrelli C., Hernández E., Molter U.

Preprint, November 2023: https://arxiv.org/abs/2311.12544

* The structure of group preserving operators.

Barbieri D., Cabrelli C., Carvajal, D., Hernández E., Molter U.

Accepted in SASIDA (Sampling Theory, Signal Processing, and Data Analisis), 19 (5), (2021). https://arxiv.org/abs/2009.12551

* Data Approximation with Time-Frequency Invariant Systems.

Barbieri D., Cabrelli C., Hernández E., Molter U. (2020)

In: Boggiatto P. et al. (eds) Landscapes of Time-Frequency Analysis.

Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-56005-8_2

* Lebesgue-type inequalities for greedy approximation,

S. Dilworth, G. Garrigós, E. Hernández. D. Kutzarova, V. Temlyakov,

J. Funct. Analysis, 280 (5), (2021). https://doi.org/10.1016/j.jfa.2020.108885

* Spaces generated by orbits of unitary representations: A tribute to Guido Weiss,

E. Hernández, P. Luthy, H. Sikic, F. Soria, E. N. Wilson,

The Journal of Geometric Analysis, 31 (9), (2021), https://doi.org/10.1007/s12220-020-00396-0

* Optimal translational-rotational invariant dictionaries for images,

D. Barbieri, C. Cabrelli, E. Hernández, U. Molter,

Wavelets and Sparsity, XVIII, SPIE 2019, 11138-3, https://arxiv.org/abs/1909.01887

* Approximation by group invariant subspaces.

D. Barbieri, C. Cabrelli, E. Hernández, U. Molter,

J. Math. Pures Appl. 142 (2020), 76-100. https://arxiv.org/abs/1907.08300

* Extra invariance of principal shift invariant spaces and the Zak transform.

D. Barbieri, E. Hernández, C. Mosquera,

Preprint, 2019. https://arxiv.org/abs/1904.10538

* Spaces invariant under unitary representations of discrete groups.

Barbieri, E. Hernández, V. Paternostro,

J. Math. Anal. Appl. 492 (1), (2020) . https://arxiv.org/abs/1811.02993

* Lebesgue inequalities for Chebyshev thresholding greedy algorithms.

P.M. Berná, O. Blasco, G. Garrigós, E. Hernández. T. Oikhberg,

Revista Matemática Complutense, 33 (2020), 695-722 https://arxiv.org/abs/1811.04268

* Calderón-type inequalities for affine frames.

D. Barbieri, E. Hernández, A. Mayeli,

Applied and Computational Harmonic Analysis, 50 (2021), 326-352. https://arxiv.org/abs/1706.06518

* Frames of exponentials and submultitiles in LCA groups.

D. Barbieri, C. Cabrelli, E. Hernández, P. Luthy, U. Molter, C. Mosquera,

C.R. Acad. Sci. Paris, Ser. 1, 356 (2018), 107-113. PDF

* Embeddings and Lebesgue-type inequalities for the greedy algorithm in Banach spaces.

P.M. Berná, O. Blasco, G. Garrigós, E. Hernández. T. Oikhberg,

Constructive Approximation, 48 (3), (2018) 415–451 http://arxiv.org/abs/1707.07513

* Lattice sub-tilings and frames in LCA groups.

D. Barbieri, E. Hernández, A. Mayeli,

C.R. Acad. Sci. Paris, Ser. 1, 356 (2), (2017), 193-199. PDF

* Riesz and Frame sequences: The bracket and the Gramian.

D. Barbieri, E. Hernández, V. Paternostro,

Collect. Math. 69 (2), (2017) 221-236, DOI 10.1007/s13348-017-0202-x PDF

* Non-commutative shift-invariant spaces.

D. Barbieri, E. Hernández, V. Paternostro,

Preprint, (2015) http://arxiv.org/pdf/1506.08942.pdf

* Results on non-linear approximation for wavelet bases in weighted function spaces.

E. Hernández, M. de Natividade,

In New Trends in Applied Harmonic Analysis, Editors, Aldroubi, Cabrelli, Jaffard, Molter, Birkhäuser (2016), 145 - 189

* Tiling by lattices for locally compact abelian groups.

D. Barbieri, E. Hernández, A. Mayeli,

Preprint, https://arxiv.org/abs/1508.04208

* The Zak transform and the structure of spaces invariant under the action of an LCA group.

D. Barbieri, E. Hernández, V. Paternostro,

Journal of Functional Analysis, 269 (5), 1327-1358, (September 2015) PDF

* Greedy bases in variable Lebesgue spaces.

D. Cruz-Uribe, SFO, E. Hernández, J. M. Martell,

Monatshefte für Mathematik, 179(3), 355-378 (March 2016). PDF

* Conditionality constants for quasi-greedy bases in super-reflexive Banach spaces.

F. Albiac, J.L. Ansorena, G. Garrigós, E. Hernández, M. Raja,

Studia Mathematica 227 (2) (January 2015), 133-140.

* Riesz and frame systems generated by unitary actions of discrete groups.

D. Barbieri, E. Hernández, J. Parcet,

Applied and Computational Harmonic Analysis, 39 (3) (November 2015), 369-399 PDF

* Bracket map for Heisenberg group and the characterization of cyclic subspaces.

D. Barbieri, E. Hernández, A. Mayeli,

Applied and Computational Harmonic Analysis, 37 (2) 2014; DOI: 10.1016/j.acha.2013.12.002 PDF

* Greedy type algortihms for RIP matrices. A study of three selection rules.

E. Hernández, D. Vera,

Preprint, 2012. . PDF

* Lebesgue type inequalities for quasi-greedy bases.

G. Garrigós,. E. Hernández, T. Oikhberg,

Constr. Approx. 38 (2013). 447-479; DOI 10.107/s00365-013-9209-z . PDF

* Lebesgue type inequalities for quasi-greedy bases.

E. Hernández, arXiv:1111.0460v2 [math.FA] 16 Nov 2011

Preprint, 2011. . PDF

* Restricted non-linear approximation in sequence spaces and applications to wavelet bases and interpolation.

E. Hernández, D. Vera

Monatshefte für Mathematik: Volume 169, Issue 2 (2013), 187-217. DOI 10.1007/s00605-012-0425-6 . PDF

* Democracy systems of translates

E. Hernández, M. Nielsen, H. Sikic, F.Soria

Journal of Approximation Theory 171 (2013) 105–127.. . PDF

* Democracy functions of wavelet bases in general Lorentz spaces.

G. Garrigós, E. Hernández , M. de Natividade.

Journal of Approx. Theory 163 (2011), 1509-1521. DOI: 10.1016/j.jat.2011.05.008, . PDF

* The Zak Transform(s).

E. Hernández, H. Sikic, G. Weiss, E. Wilson

Wavelets and Multiscale Analysis, Applied and Numerical Harmonic Analysis, 2011, Part I, 151-157. . PDF

* Democracy functions and optimal embeddings for Approximation spaces.

G. Garrigós, E. Hernández, M. de Natividade.

Advances in Computational Mathematics: Volume 37, Issue 2 (2012), 255-283, doi:10.1007/s10444-011-9197-0 . PDF

* Quantifying democracy for wavelet bases in Lorentz spaces.

E. Hernández, J.M. Martell, M. de Natividade

Constructive Approximation: Volume 33, Issue 1 (2011), Page 1-14. DOI: 10.1007/s00365-010-9113-8. PDF

* Cyclic subspaces for unitary representations of LCA groups: generalized Zak transform.

E. Hernández, H. Sikic, G. Weiss, E. Wilson

Proceedings of the Conference in honor of A. Hulaniki, Poland, 2009.. Colloq. Math. 118 (2010), no.1, 313-332. . PDF

* Proceedings of the 8th Internatioanl Conference on Harmonic Analysis and Partial Differential Equations

P. Cifuentes, J. García-Cuerva, G. Garrigós, E. Hernández, J.M. Martell, J. Parcet, A. Ruiz, F. Soria, J. L. Torrea, A. Vargas (Editors),

Contemporary Mathematics, American Mathematical Society, no 505, (2010)

* On the properties of the integer translates of a square integrable function in L²(R).

E. Hernández, H. Sikic, G. Weiss, E. Wilson

Comtemp. Math. 505, (2010), 233-249., 2008. PDF

* Wavelets, Orlicz spaces, and Greedy Bases.

G. Garrigós, E. Hernández, J. M. Martell.

App. and Comp. Harmonic Analysis, 24, (2008), 70-93, doi: 10.1016/j.acha.2007.06.001. PDF

* Proceedings of the 7th Internatioanl Conference on Harmonic Analysis and Partial Differential Equations

P. Cifuentes, J. García-Cuerva, E. Hernández, K. Kazarian, F. Soria, J. L. Torrea, A. Vargas (Editors)

Collectanea Mathematica,, Universitat de Barcelona, 2006.

* Further results on the connectivity of Parseval frame wavelets.

G. Garrigós, E. Hernández, H. Sikic, F. Soria.

(Proceedings of the Amer. Math. Soc., 134 (2006), 3211-3221.) PDF

* Sharp Jackson and Bernstein inequalities for N-term approximation in sequences spaces with applications.

G. Garrigós, E. Hernández,

Ind. Univ. Math. J. 53, No. 6, (2004), 1741-1764. PDF

* Oversampling, Quasi Affine Frames and Wave Packets.

E. Hernández, D. Labate, G. Weiss, E. Wilson,

Applied and Computational Harmonic Analysis, 16 (2004), 111-147. PDF

* Connectivity in the set of Tight Frame Wavelets (TFW).

G. Garrigós, E. Hernández, H. Sikic, F. Soria, G. Weiss, E. Wilson,

Glasnik Matematicki, Vol. 38 (58), (2003), 75-98. PDF

* Ondículas y tecnología.

E. Hernández, Bol. Soc. Esp. Mat. Apl., nº 25 (2003), 39-54. PDF

* Proceedings of the 6^th International Conference on Harmonic Analysis and Partial Differential Equations.

P. Cifuentes, J. García-Cuerva, E. Hernández, F. Soria, J. L. Torrea, A. Vargas (Editors),

Publications Matemàtiques, Universitat Autònoma de Barcelona, 2002.

* A unified characterization of reproducing systems generated by a finite family, II.

E. Hernández, D. Labate, G. Weiss,

The J. of Geometric Analysis, Volume 12, Number 4, (2002), 615-662. PDF

* Basic properties of wavelets.

The Wutam consortium, J. of Fourier Anal. and Appl.., Vol. 4, no 4 (1998), 575-594.

* Characterization of wavelets, scaling functions and wavelets associated with a Multiresolution Analysis.

E. Hernández, X. Wang, G. Weiss,

Israel Mathematical Conference. Proceedings (AMS Publication)., Vol. 13 (1999), 51-87.

* Interpolation of Herz spaces and applications,

E. Hernández, D. Yang,

Mathematische Nachrichten, Vol. 205 (1999), 69-87. PDF

* Interpolation of Herz-type Hardy spaces,

E. Hernández, D. Yang,

Illinois J. of Math., Vol. 42 (4) ( 1998), 564-581.

* Band-limited wavelets with subexponential decay,

J. Diziubansky, E. Hernández,

Canadian Math. Bulletin, Vol.41(4) (1998), 398-403. PDF

* Smoothing minimally supported frecuency (MSF) wavelets: Part II,

E. Hernández, X. Wang, G. Weiss,

J. of Fourier Anal. and Appl., Vol. 3 no 1 (1997), 23-40. PDF

* The j-transform an wavelet characterization of Herz-type spaces,

E. Hernández, G. Weiss, D. Yang,

Collectanea Matematica, Vol. 48 no 3 (1996), 285-320.

* A first course on wavelets,

E. Hernández, G. Weiss,

CRC Press , (1996), 489 páginas (ISBN: 0-8493-8274-2).

* Smoothing minimally supported frecuency (MSF) wavelets: Part I,

E. Hernández, X. Wang, G. Weiss,

J. of Fourier Anal. and Appl., Vol. 2 no 4 (1996), 229-340. PDF

* Fourier Analysis and Partial Differential Equations,

J. García-Cuerva, E. Hernández, F. Soria, J.L. Torrea (Editores),

Studies in Advanced Mathematics, CRC Press, (1995),ISBN:0-8493-7877-X

* Interpolation theorems for some weighted quasi-Banach spaces,

E. Hernández, J. Soria,

Israel Conference Mathematical Proceedings, AMS Publication , Vol 5 (1992), 61-80.

* Estimates for the Kakeya maximal operator on radial functions in Rⁿ,

A. Carbery, E. Hernández, F. Soria,

ICM-90 Satellite Conference in Harmonic Analysis. Springer –Verlag (1991), 41-50.

* Spaces of Lorentz type and complex interpolation,

E. Hernández, J. Soria,

Arkiv für Matematik, Vol. 29 no 2 (1991), 203-220.

* Weighted inequalities throught factorization,

E. Hernández,

Publicacions Matemàtiques, Vol. 35 (1991), 141-153.

* The behaviour on radial functions of maximal operators along arbitrary directions and the Kakeya maximal operator,

A. Carbery, E. Hernández, F. Soria,

Tohuku Math. Journal, Vol. 41, (1989), 647-656.

* Factorization and extrapolation of pairs of weights,

E. Hernández,

Studia Math. Vol XCV, nº 2, (1989), 77-91.

* Interpolation of subspaces and quotient spaces,

E. Hernández, R. Rochberg, G. Weiss,

Function spaces and applications. Lecture Notes in Math. 1302, Springer-Verlag, (1988), 253-289

* Intermediate spaces and the complex method of interpolation for families of Banach spaces,

E. Hernández,

Annali Escuola Normale Superiore, Pisa (Clase de Scienze), Serie IV, Vol. 12 (1986), 245-265.

* A relation between two interpolation methods,

E. Hernández,

Interpolation theory and allied questions in analysis. Lecture Notes in Math. 1070, Springer-Verlag, (1984), 80-91.

* An interpolation theorem for analytic families of operators acting on certain H^pspaces,

E. Hernández,

Pac. J. of Math., 110 (1984), 213-220. PDF