Research

Member of the research group Harmonic Analysis and Fractal Geometry

Research interests:

Harmonic Analysis
Frame theory
Group Shift-Invariant spaces
Fourier Analysis on locally compact groups
Sampling and Dynamical sampling

Journal papers:

E. King, R. Nores and V. Paternostro, The density of Gabor systems in expansible locally compact abelian groups. Preprint. PDF.
A. Aguilera, C. Cabrelli, D. Carbajal and V. Paternostro, Reducing and Invariant subspaces under two commuting shift operators, J. Math. Anal. Appl., 528, (2023), 1, 127481. PDF
A. Aguilera, C. Cabrelli, D. Carbajal and V. Paternostro, Frames by iterations of two operators that commute, Appl. Comput. Harmonic Anal., 66, (2023), 46-61. PDF
D. Kosz, J. Martínez Perales, V. Paternostro, E. Rela and L. Roncal, Maximal operators on the infinite-dimensional torus, Math. Ann., 385, (2023), 1-39. PDF
A. Aguilera, C. Cabrelli, D. Carbajal and V. Paternostro, Diagonalization of shift-preserving operators, Adv. Math., 389 (2021), Paper No. 107892. PDF
C. Cabrelli, C. Mosquera and V. Paternostro, Extra-invariance of group actions, J. Geom. Anal., 31, (2021), 11878-11898. PDF
A. Aguilera, C. Cabrelli, D. Carbajal and V. Paternostro, Dynamical Sampling for shift-preserving operators, Appl. Comput. Harmonic Anal., 51, (2021), 258-274. PDF
D. Barbieri, E. Hernández and V. Paternostro, Spaces invariant under unitary representations of discrete groups, J. Math. Anal. Appl., 492, (2020), 1, 124357, 32 pp. PDF.
C. Cabrelli, U. Molter, V. Paternostro and F. Philipp, Dynamical Sampling on finite index sets, Journal d’Analyse Mathematique, 140, (2020), 637–667. PDF.
V. Paternostro and E. Rela, Improved Buckley's Theorem on locally compact abelian groups, Pacific J. Math., 299 (2019), 1, 171–189. (DOI 10.2140/pjm.2019.299.171). PDF.
D. Barbieri, E. Hernández and V. Paternostro, Group Riesz and Frame Sequences: The Bracket and the Gramian, Collectanea Mathematica, 69, (2018), 2, 221–236. PDF.
G. Kutyniok, V. Paternostro and F. Philipp, The effect of perturbations of operator-valued frame sequences and fusion frames on their duals, Operators and Matrices, 11, (2017), 2, 301–336. PDF.
C. Cabrelli, C. Mosquera and V. Paternostro, An Approximation Problem in Multiplicatively Invariant Spaces, Contemp. Math., 693, (2017), 143–165. PDF.
D. Barbieri, E. Hernández and V. Paternostro, The Zak transform and the structure of spaces invariant by the action of an LCA group, J. Funct. Anal. 269, (2015), 5, 1327-1358. PDF.
V. Paternostro, Linear combinations of generators in multiplicatively invariant spaces, Studia Math. 226, (2015), 1, 1-16. PDF.
C. Cabrelli, C. Mosquera and V. Paternostro, Linear combinations of frames generators in systems of translates, J. Math. Anal. Appl. 413, (2014), 2, 776--788. PDF.
S. Heineken, E. Matusiak and V. Paternostro, Perturbation of frame sequences: canonical dual systems, approximate reconstructions and applications, Int. J. Wavelets Multiresolut. Inf. Process., 12}, (2014), 2. PDF.
C. Cabrelli and V. Paternostro, Shift-Modulation Invariant Spaces on LCA Groups, Studia Math. 211, (2012), 1, 1--19. PDF.
M. Anastasio, C. Cabrelli, V. Paternostro, Invariance of a Shift-Invariant Space in several variables, Complex Anal. Oper. Theory 5, (2011), 4, 1031-1050. PDF.
M. Anastasio, C. Cabrelli, V. Paternostro, Extra invariance of shift-invariant spaces on LCA groups, J. Math. Anal. Appl. 370, (2010), 2, 530--537. PDF.
C. Cabrelli and V. Paternostro, Shift-Invariant Spaces on LCA Groups, J. Funct. Anal. 258, (2010), 6, 2034--2059. PDF.

Proceedings:

A. Aguilera, C. Cabrelli, D. Carbajal and V. Paternostro, Frames by Iterations in Shift-invariant Spaces, 13th International Conference on Sampling Theory and Applications (SampTA’19, Bordeaux, Francia, 2019). Por aparecer. PDF.
C. Cabrelli, U. Molter, V. Paternostro and F. Philipp, Finite Sensor Dynamical Sampling, 12th International Conference on Sampling Theory and Applications (SampTA'17), IEEE Xplore, (2017), 50–54. PDF.
G. Kutyniok, V. Paternostro and F. Philipp, Perturbations of Fusion Frames and the Effect on Their Canonical Dual, Proc. SPIE Optical Engineering+ Applications, (2015), 95970S-95970S-7. PDF.
I. Bojarovska and V. Paternostro, Gabor fusion frames generated by difference sets, Proc. SPIE Optical Engineering+ Applications, (2015), 95970D-95970D-14. PDF.

Other publications:

D. Barbieri, E. Hernández and V. Paternostro, Noncommutative Shift-Invariant Spaces, (2015), PDF.
PhD Thesis: Estuctura y propiedades de espacios invariables por traslaciones en grupos abelianos localmente compactos.
Tesis de Licenciatura (Spanish): Teorema de Balian-Low. PDF.