Papers

• D. Barbieri, C. Cabrelli, E. Hernández, U. Molter, Learning optimal smooth invariant subspaces for data approximation. Journal of Mathematical Analysis and Applications (to appear, 2024). arXiv

• D. Barbieri, Reconstructing group wavelet transform from feature maps with a reproducing kernel iteration. Frontiers in Computational Neuroscience, 2022. open, doi, arXiv

• D. Barbieri, C. Cabrelli, D. Carbajal, E. Hernández, U. Molter, The structure of group preserving operators. Sampling Theory Signal Processing, and Data Analysis 19:5, 2021. doi, arXiv 

• D. Barbieri, E. Hernández, A. Mayeli, Calderón-type inequalities for affine frames. Applied and Computational Harmonic Analysis 50:326-352, 2021. doi, arXiv

• D. Barbieri, C. Cabrelli, E. Hernández, U. Molter, Approximation by group invariant subspaces. Journal de Mathématiques Pures et Appliquées 142:76-100, 2020. doi, arXiv

• D. Barbieri, E. Hernández, V. Paternostro, Spaces invariant under unitary representations of discrete groups. Journal of Mathematical Analysis and Applications 492:124357, 2020. doi, arXiv

• D. Barbieri, C. Cabrelli, E. Hernández, U. Molter, Data approximation with time-frequency invariant systems. In "Landscapes of Time-Frequency Analysis, Vol.2", P. Boggiatto, T. Bruno, E. Cordero, H. G. Feichtinger, F. Nicola, A. Oliaro, A. Tabacco, M. Vallarino (eds). Applied and Numerical Harmonic Analysis, Birkhäuser, 2020. doi, arXiv

• D. Barbieri, C. Cabrelli, E. Hernández, U. Molter, Optimal translational-rotational invariant dictionaries for images. In "Wavelets and Sparsity XVIII", D. Van De Ville, M. Papadakis, Y. M. Lu (eds). Proceedings of SPIE 11138, 2019. doi, arXiv

• D. Barbieri, C. Cabrelli, E. Hernández, P. Luthy, U. Molter, C. Mosquera, Frames of exponentials and sub-multitiles in LCA groups. Comptes Rendus Mathématique 356:107-113, 2018. doi, arXiv

• D. Barbieri, E. Hernández, V. Paternostro, Group Riesz and frame sequences: the bracket and the Gramian. Collectanea Mathematica 69:221-236, 2018. doi, arXiv

• A. Sarti, D. Barbieri, Neuromorphology of meaning. In "Quantitative semiotic analysis", D. Compagno (ed). Lecture Notes in Morphogenesis, Springer, 2018. doi

• D. Barbieri, E. Hérnandez, A. Mayeli, Lattice sub-tilings and frames in LCA groups. Comptes Rendus Mathématique 355:193-199, 2017. doi, arXiv

• D. Barbieri, Geometry and dimensionality reduction of feature spaces in primary visual cortex. In "Wavelets and Sparsity XVI", M. Papadakis, V. K. Goyal, D. Van De Ville (eds). Proceedings of SPIE 9597, 2015. doi, arXiv

• D. Barbieri, E. Hernández, V. Paternostro, The Zak transform and the structure of spaces invariant by the action of an LCA group. Journal of Functional Analysis 269:1327-1358, 2015. doi, arXiv

• G. Cocci, D. Barbieri, G. Citti, A. Sarti, Cortical spatio-temporal dimensionality reduction for visual grouping. Neural Computation 27:1252-1293, 2015. doi, arXiv

• D. Barbieri, E. Hernández, J. Parcet, Riesz and frame systems generated by unitary actions of discrete groups. Applied and Computational Harmonic Analysis 39:369-399, 2015. doi, arXiv

• D. Barbieri, G. Citti, Reproducing kernel Hilbert spaces of CR functions for the Euclidean Motion group. Analysis and Applications 13:331-346, 2015. doi, arXiv

• D. Barbieri, G. Citti, A. Sarti, How uncertainty bounds the shape index of simple cells. The Journal of Mathematical Neuroscience 4:5, 2014. doi, arXiv

• D. Barbieri, E. Hernández, A. Mayeli, Bracket map for Heisenberg group and the characterization of cyclic subspaces. Applied and Computational Harmonic Analysis 37:218-234, 2014. doi, arXiv

• D. Barbieri, G. Citti, G. Cocci, A. Sarti, A cortical-inspired geometry for contour perception and motion integration. Journal of Mathematical Imaging and Vision 49:511-529, 2014. doi, arXiv

• D. Barbieri, G. Citti, G. Sanguinetti, A. Sarti, An uncertainty principle underlying the functional architecture of V1. Journal of Physiology, Paris 106:183-193, 2012. doi, pdf

• G. Cocci, D. Barbieri, A. Sarti, Spatio-temporal receptive fields of cells in V1 are optimally shaped for stimulus velocity estimation. Journal of the Optical Society of America A 29:130-138, 2012. doi, pdf

• D. Barbieri, G.Citti, Regularity of minimal intrinsic graphs in 3 dimensional sub-Riemannian structures of step 2. Journal de Mathématiques Pures et Appliquées 96:279-306, 2011. doi, arXiv

• D. Barbieri, Approximations of Sobolev norms in Carnot groups. Communications in Contemporary Mathematics 13:765-794, 2011. doi, arXiv

• D. Barbieri, A. Vivoli, Long-range correlations in time series generated by time-fractional diffusion: a numerical study. Physica A 355:190-198, 2005. doi, pdf

Other preprints

• D. Barbieri, E. Hernández, C. Mosquera, Extra-invariance of principal shift-invariant spaces and the Zak transform. arXiv

• D. Barbieri, E. Hernández, V. Paternostro, Noncommutative Shift-Invariant Spaces. arXiv

• D. Barbieri, E. Hernández, A. Mayeli, Tiling by lattices for locally compact abelian groups. arXiv

• D. Barbieri, G. Citti, G. Sanguinetti, A. Sarti, Coherent states of the Euclidean group and activation regions of primary visual cortex. arXiv