caa a22 4500 463247086 CHVBK 20180405153329.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s00041-006-6044-7 doi (NATIONALLICENCE)springer-10.1007/s00041-006-6044-7 Multiscale Haar Orthonormal Matrices with the Corresponding Riesz Productsand a Characterization of Cantor-Type Languages [Elektronische Daten] [N.D. Atreas, C. Karanikas] We introduce a class of multiscale orthonormal matrices H(m) of order m×m, m = 2, 3,... . For m = 2 N, N = 1, 2,..., we get the well known Haar wavelet system. The term "multiscale" indicates that the construction of H(m) is achieved in different scales by an iteration process, determined through the prime integer factorization of m and by repetitive dilation and translation operations on matrices. The new Haar transforms allow us to detect the underlying ergodic structures on a class of Cantor-type sets or languages. We give a sufficient condition on finite data of lengthm, or step functions determined on the intervals [k/m, (k + 1)/m) , k = 0,...,m − 1 of [0, 1), to be written as a Riesz-type product in terms of the rows of H(m). This allows us to approximate in the weak-* topology continuous measures by Riesz-type products. Birkhauser Boston, 2007 Atreas N.D. Technological Institution of West Macedonia, Department of General Sciences, 501-00 Koila Kozanis, Kozani, Greece aut Karanikas C. Department of Informatics, Aristotle University of Thessaloniki, 54-124, Thessaloniki, Greece aut Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/2(2007-04-01), 197-210 1069-5869 13:2<197 2007 13 41 https://doi.org/10.1007/s00041-006-6044-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6044-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Atreas N.D. Technological Institution of West Macedonia, Department of General Sciences, 501-00 Koila Kozanis, Kozani, Greece aut NATIONALLICENCE 700 1- Karanikas C. Department of Informatics, Aristotle University of Thessaloniki, 54-124, Thessaloniki, Greece aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/2(2007-04-01), 197-210 1069-5869 13:2<197 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer