RESEARCH GROUP ON HARMONIC ANALYSIS Publications

Publications:

Journal Papers

Barrozo, M. F. and Molter, U.“Countable contraction mappings in metric spaces: invariant sets and measure”, Cent. Eur. J. Math., 2014, 12(4), 593-602. pdf-file.
Cabrelli C., Mosquera C. A., Paternostro, V.“Linear combinations of frame generators in systems of translates”. To appear in J. Math. Anal. Appl.pdf-file.
Heineken S., Matusiak E., Paternostro, V.“Perturbed frame sequences: canonical dual systems, approximate reconstructions and applications”. To appear in International Journal of Wavelets, Multiresolution and Information Processing.
Carrizo I., Heineken S.“Critical pairs of sequences of a mixed frame potential.”. To appear in Numerical Functional Analysis and Optimization.pdf-file.
Cabrelli C., Paternostro, V.“Shift-modulation invariant spaces on LCA groups”. Studia Mathematica. Vol. 211, 2012, pg. 1-19.pdf-file.
Balan, R., Christensen, J., Krishtal, I., Okoudjou, K., Romero, J. L.“Multi-window Gabor frames in amalgam spaces”. Preprint.pdf-file.
Cabrelli, C., Molter, U. and Romero, J. L.“Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces”. Advances in Mathematics. Vol. 232, Issue 1, Jan. 2013, pg. 98-120.pdf-file.
Hare, K., Mendivil, F. and Zuberman, L..“The sizes of rearrangements of Cantor sets”. Canadian Mathematical Bulletin. To appear. pdf-file.
Balazs, P., Cabrelli, C., Heineken, S. and Molter, U. “Frames by Multiplication”. Current Developments in Theory and Applications of Wavelets. Current Development in Theory and Applications of Wavelets, Vol. 5, 2011, pg. 165-186.pdf-file.
Garcia, I. and Zuberman, L.“Exact packing measure of central Cantor sets in the line”. Journal of Mathematical Analysis and Applications. To appear. pdf-file.
Molter U. , Rela E. “Furstenberg sets for a fractal set of directions” Proceedings of the American Mathematical Society. To appear 2011.pdf-file.
Anastasio M. , Cabrelli C., Paternostro V. “Invariance of a shift-invariant space in several variables.” Complex Anal. Oper. Theory, To appear. 2011.pdf-file.
Aldroubi, A., Anastasio, M., Cabrelli, C., Molter, U., “A dimension reduction scheme for the computation of optimal unions of subspaces.” Sampling Theory in Signal and Image Processing., 10 (1-2) (2011) pp. 135 - 150.pdf-file.
Hare, K. and Zuberman, L. “Classifying Cantor sets by their multifractal spectrum”. Nonlinearity, 23 (11) (2010) pp. 2919--2933.pdf-file.
Cabrelli, C. , Hare, K. , Molter, U. “Classifying Cantor sets by their fractal dimensions”. Proceedings of the American Mathematical Society, 138 (11) (2010) pp. 3965-3974.pdf-file.
Romero, J. L. “Characterization of coorbit spaces with phase-space covers.” Journal of Functional Analysis. Vol. 262, Issue 1, Jan. 2012, pg. 59-93.pdf-file.
Molter U. , Rela E. “Small Furstenberg sets.” Journal of Mathematical Analysis and Applications. To appear. pdf-file.
Feichtinger, H. G., Príncipe J. C., Romero J. L., Singh Alvarado, A., Velasco, G. A. “Approximate reconstruction of bandlimited functions for the integrate and fire sampler ” Advances in Computational Mathematics. Vol.36 No.1 (2012) p.67--78.pdf-file.
Romero, J. L. “Surgery of spline-type and molecular frames.” Journal of Fourier Analysis and Applications. Vol. 17, Issue 1 Feb. 2011, pg. 135-174.pdf-file.
Cabrelli C. , Paternostro V. “Shift Invariant Spaces on LCA Groups.” Journal of Functional Analysis". Vol 258, Issue 6, 15, March 2010, pp 2034--2059.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.”Journal of Mathematical Analysis and Aplications". Vol 370, Issue 2, 15, October 2010, pp 530-537.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. Vol 16, No 1, pp 60-75, 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. pdf-file.
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.
Molter, U. M. “Medidas tangenciales sobre cuerpos convexos en E3”. Matemática Notae, 31: 81 - 97, 1988.
Cabrelli, C. A. “The Error in Least Square Shaping Filter”. Revista de la UMA, 33 (1), 1987.
Molter, U. M. “A Generalization of the Fundamental Formula for Cylinders”. Revista de la UMA, 32 (4), 244-248, 1987.pdf-file.
Molter, U. M. “Tangential Measures on the Set of Convex Infinite Cylinders”. Journal of Applied Probability, 23: 961 - 972, 1986.pdf-file.
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

Cabrelli C., Darji, U., Molter, U.“Visible and Invisible Cantor sets”.Invited Chapter in Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center. Editors: Travis Andrews, Radu Balan, Wojciech Czaja, Kasso Okoudjou, John Benedetto Publisher: Springer.pdf-file.
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.

Edited Books

Cabrelli, C. and Torrea, J. L. (Eds.) “Recent developments in real and harmonic analysis”. In honor of Carlos Segovia (English). Applied and Numerical Harmonic Analysis. Boston, MA. Birkhäuser. xxii, 193 p. (2010).
Aldroubi, A., Cabrelli, C., Jaffard, S. and Molter, U. (Eds.) “New Trends in Applied Harmonic Analysis”. Applied and Numerical Harmonic Analysis. Birkhäuser. 356 p. (2017).pdf-file.
Aldroubi, A., Cabrelli, C., Jaffard, S. and Molter, U. (Eds.) “New Trends in Applied Harmonic Analysis, Volume 2”. Applied and Numerical Harmonic Analysis. Birkhäuser. 320 p. (2019).pdf-file.