Grupo de Investigación en
Análisis Real y Armónico
Muestreo, Wavelets y Geometría Fractal

•  Inicio 
•  Miembros 
•  Publicaciones 
•  Seminarios 
•  Congresos 
•  Fotos 

  

Publications

Journal Papers

• Romero, J. L. ``Surgery of spline-type and molecular frames.'' Journal of Fourier Analysis and Applications. To appear. pdf-file.
• Cabrelli C. , Paternostro V. ``Shift Invariant Spaces on LCA Groups.'' Journal of Functional Analysis. To appear. pdf-file.
• Anastasio M. , Cabrelli C. ``Sampling in a Union of Frame Generated Subspaces.'' Sampling Theory in Signal and Image Processing. Vol 8. No. 3. Sep. 2009. pp. 261-286. pdf-file.
• Anastasio M. , Cabrelli C., Paternostro V. ``Extra invariance of shift invariant spaces on LCA groups.'' Preprint. 2009. pdf-file.
• Anastasio M. , Cabrelli C., Paternostro V. ``Invariance of a shift-invariant space in several variables.'' Preprint. 2009. pdf-file.
• Molter U. , Rela E. ``Improving dimension estimates for Furstenberg-type sets.'' Advances in Mathematics 223 (2010) pp. 672-688. pdf-file.
• Romero, J. L. ``Explicit localization estimates for spline-type spaces.'' Sampling Theory in Signal and Image Processing. Vol 8. No. 3. p.249-259, 2009. pdf-file.
• Aldroubi A. , Cabrelli C. , Heil C. , Kornelson K, Molter U. ``Invariance of a Shift-Invariant Space.'' Journal of Fourier Analysis and Applications. To appear. pdf-file.
• Cabrelli, C. , Molter, U. M. Hare, K. E. ``Classifying Cantor Sets by their Fractal Dimensions.'' Proceedings of the AMS. to appear 2010. pdf-file.
• Molter, U. Zuberman, L. ``A fractal Plancherel Theorem.'' Real Analysis Exchange. 14,(34) 69-86, 2008/2009. pdf-file.
• Feichtinger, H. G. , Molter, U. , Romero, J. L. ``Perturbation techniques in spline-type spaces.'' International Journal of Wavelets, Multiresolution and Information Processing. Special Issue on Multiscale Methods, Sparse Decompositions and Parsimonious Statistics. 2,(6) 249-277, 2008. pdf-file.
• Aldroubi, A. , Cabrelli, C. , Molter, U.M. ``Optimal Non-Linear Models for Sparsity and Sampling.'' Journal of Fourier Analysis and Applications. 14,(5) 793-812, 2008. pdf-file.
• García, I. , Molter, U.M. , Scotto, R. "Dimension Functions of Cantor sets". Proceedings of the American Mathematical Society, 135 (10) (2007) . pdf-file.
• Aldroubi, A. , Cabrelli, C. , Hardin, D. and Molter, U.M. "Optimal shift invariant spaces and their Parseval frame generators". Applied and Computational Harmonic Analysis, 23 (2) (2007). pdf-file.
• Cabrelli, C. , Molter, U.M. ``Density of the Set of Generators of Wavelets Systems'', Constructive Approximation, 26 (1) (2007). pdf-file.  
• Cabrelli, C. , Molter, U.M. ``¿Ondículas, Wavelets? Una buena señal'' (in spanish), Ciencia Hoy, 16 (95) (2006), 22 -- 34.   htm-file
• Blanco C., Cabrelli, C. and Heineken S., "Functions in Sampling Spaces" Sampling Theory in Signal and Image Processing, 5 (3) (2005), 275 -- 295.   pdf-file.
• Cabrelli, C., Lacey, M., Molter, U.M. and Pipher, J. "Variations on the Theme of Journe's Lemma". Houston Journal of Mathematics, Electronic Edition. 32 (3) (2006) 833--861.
• Cabrelli, C. , Heineken, S. , Molter, U. M. "Local Bases for Refinable Spaces". Proceedings of the AMS. 134 (2006) 1707-1718. pdf-file.
• Cabrelli, C. , Molter, U.M. ``Geometric Methods in Wavelet Theory'', Revista de la UMA , 46 (2) (2005), 121-132.   pdf-file.
• Cabrelli, C. , Heineken, S. , Molter, U. M. "Refinable Shift Invariant Spaces in R^n". International Journal of Wavelets, Multiresolution and Information Processing. Special issue on "Sampling and Frames in Wavelet Theory and Time-Frequency Analysis" 3 (2005), 3, 321-345. pdf file
• Aldroubi, A. , Cabrelli, C. , Molter, U. " Wavelets on Irregular Grids with Arbitrary Dilation Matrices, and Frame Atoms for L2(Rd)". Applied and Computational Harmonic Analysis. Special Issue on Frames II. 119-140 (2004)   pdf-file.
• Cabrelli, C. A. Heil, C. and Molter, U. M. "Self-Similarity and Multiwavelets in Higher Dimensions". Memoirs of the AMS. 170 (807) 82p. 2004 .  gzipped-pdf-file.
• Cabrelli, C. , Mendevil, F. , Molter, U., Shonkwiler, R. " On the Hausdorff h-Measure of Cantor Sets". Pacific Journal of Mathematics. 217(1)45-59. (2004) pdf-file.
• Benavente, A. , Cabrelli, C., "Finitely Generated Multiresolution Analysis in Several Variables" . Revista de la Union Matemática Argentina. 44 (1) (75-88) (2003) pdf-file.
• Cabrelli, C. A.,Molter, U. M., Paulauskas, V. and Shonkwiler, R. "The Hausdorff dimension of p-Cantor sets". Real Analysis Exchange. 30 (2004/05) nr.2 413-433.    pdf-file.
• Romero, E. "A Complete gabor System of Zero Beurling Density". Sampling Theory in Signal and Image Processing. 1 nr.1 (2002) 299-304.    pdf-file.
• Cabrelli, C. A., Hare, K. E. and Molter, U. M. "Sums of Cantor Sets yielding an interval". Journal of the Australian Mathematical Society. Series A. 73 (3), 405-418, (2002)     pdf-file.
• Cabrelli, C. A., Falsetti, M. y Molter, U. M. "Fractal Block-coding: A functional approach for Image and Signal Processing''. Computers and Mathematics with applications. 44(8-9): 1183-1200,  2002.    pdf-file.
• Cabrelli, C. A., Gordillo, M. L.  "Existence of multiwavelets in $\Bbb R\sp n$. Proceedings of the AMS. 130 (5)1413--1424 (2001) (electronic).     pdf-file.
• Cabrelli,C. A., Heil, C. and Molter,U. M. "Accuracy of Multiple Refinable Distributions".  Journal of Fourier Analysis and Applications, 6 (5): 213-245, 2000.   pdf-file.
• Cabrelli, C. A., Molter, U. M. and Shonkwiler, Ron . "A CoRD (Constructive Recursive Algoritm) for neural networks on the plane". IEEE, Transactions on Neural Networks, (4):345 - 356, 2000.   pdf-file.
• Cabrelli, C. A. and Molter, U. M. "Generalized Self-Similarity". Journal of Mathematical Analysis and Applications, 230: 251 - 260, 1999.   pdf-file.
• Cabrelli, C. A. , Heil, C. and Molter, U. M. "Accuracy of Lattice Translates of Several Multidimensional Refinable Functions".  Journal of Approximation Theory, 95: 5 - 52, 1998.  pdf-file.
• Cabrelli, C. A. and Molter, U. M. "A linear time algorithm for the computation of the Kantorovich distance on the circle". Information Processing Letters, 66(3):161 - 164, 1998.  pdf-file.
• Belogay, E., Cabrelli, C. A., Molter, U. M. and Shonkwiler, R. "Calculating the Hausdorff Distance between Curves". Information Processing Letters, 64 (1):17 - 22, 1997.   pdf-file.
• Cabrelli, C. A. , Hare, K. E. and Molter, U. M. "Sums of Cantor Sets". Ergodic Theory and Dynamical Systems, 17 (6): 1299 - 1313, 1997.   pdf-file.
• Cabrelli, C. A. and Molter, U. M. "Wavelet Transform of the Dilation Equation". Journal of the Australian Mathematical Society, Series B, 37: 474 - 489, 1996.   pdf-file.
• Barahona, F., Cabrelli, C. A. and Molter, U. M. "Matching Probability Measures under Translations". Random and Computational Dynamics, 3 (3):121 - 135, 1995.     pdf-file.
• Cabrelli, C. A. and Molter, U. M. "The Kantorovich metric for probability measures on the unit circle". Computational and Applied Mathematics, 57: 345 - 361, 1995.   pdf-file.
• Cabrelli, C. A. , Forte, B., Molter, U. M. and Vrscay, E. R. "Iterated fuzzy set systems: A new approach to the inverse problem for fractals and other sets". Journal of Mathematical Analysis and Applications, 171:79 -- 100, 1992.  pdf-file.
• Barahona, F., Cabrelli, C. A. and Molter, U. M. "Computing the Hutchinson distance by network flow methods". Random and Computational Dynamics, 1(1):117 - 129, 1992.   pdf-file.
• Brandt, J., Cabrelli, C. A. and Molter, U. M. "An algorithm for the computation of the Hutchinson distance". Information Processing Letters, 40 (2):113--117, 1991.  
• Cabrelli, C. A. and Molter, U. M. "Automatic representation of binary images". IEEE: Pattern Analysis and Machine Intelligence, 12 (12): 1190--1196, 1990.  pdf-file.
• Cabrelli, C. A. ``The Error in Least Square Shaping Filter''. Revista de la UMA, 33 (1), 1987. 
• Cabrelli, C. A. ``Minimum Entropy Deconvolution and Simplicity: A noniterative Algorithm''. Geophysics, 50 (3): 394--413, 1984.  pdf-file.

Papers in Conference Proceedings

• Cabrelli, C. A , Heil, C. and Molter, U.M. "Necessary conditions for the existence of multidimensional refinable functions". Wavelets in Image and Signal Processing, A.Aldroubi, M.Laine, M.Unser editors, Proceedings of SPIEE (2000), 2000. pdf-file.
• Cabrelli, C. A., Heil, C. and Molter, U. M. "Generalized Self-Similarity applied to Matrix Refinement Equations". (resumen ampliado), Z. Angew. Math. Mech. 76: 493 - 494, 1996.
• Cabrelli, C. A. and Molter, U. M. "A Functional Equation, Wavelets and Self-Similarity". En Proceedings of the 14th imacs World Congress on Computational and Applied Mathematics, W.F.Ames, editor, (1) pp. 62 - 64, Julio 1994.
• Cabrelli, C. A. and Molter, U. M. "Density of fuzzy attractors: A step towards the solution of the inverse problem for fractals and other sets". En Proceedings of the NATO ASI on Probabilistic and Stochastic methods in analysis with applications, J.S. Byrnes, editor, Kluwer Academic Publishers, 163 - 173, 1992. pdf-file.

Invited Book Chapters

• Aldroubi, A., Cabrelli, C. A and Molter, U. M. "Learning the Right Model from the Data". Invited Chapter in Harmonic Analysis and Applications. In Honor of John J. Benedetto. C. Heil, ed., Birkhäuser, Boston, (2006): 325 -- 334. pdf-file.
• Aldroubi, A., Cabrelli, C. A and Molter, U. M. "How to construct Wavelet Frames on irregular grids and arbitrary dilations in $R^n$". Invited Chapter in Wavelets, Frames and Operator Theory. C.Heil, P. Joergensen, D. Larson eds. Contemporary Mathematics. ( 345) 1 -- 9, 2004. pdf-file.
• Aldroubi, A., Cabrelli, C. A, Hardin, D., Molter, U. M.and Rodado, A.. "Determining sets of shift invariant spaces" Proceedings of ICWA, Chennai, India, 2004. pdf-file.
• Cabrelli, C. A., Heil, C. y Molter, U. M.."Multiwavelets in Rn with an arbitrary dilation matrix". Wavelets and Signal Processing, L. Debnath editor, Birkhäuser, Basel(2003). pdf-file.
• Cabrelli, C. A., Heil, C. and Molter, U. M. "Polynomial Reproduction by Refinable Functions". Invited chapter in Advances in Wavelets, K.-S. Lau editor, Springer Verlag, New York. 121 - 163, 1999. pdf-file.
• Cabrelli, C. A., Molter, U. M. and Vrscay, E. R. "Recurrent iterated function systems: Invariant measures, a collage theorem and moment relations". En Fractal in the Fundamental and Applied Sciences, H.-O. Peitgen, J.M. Henriques & L.F.Penedo (Editors), Elsevier Science Publishers B.V. (North-Holland), pp.71 - 80, 1991. pdf-file.