In this paper we outline the main ideas behind the recent proof of the authors that if a multivariate, multi-function refinement equation with an arbitrary dilation matrix has a continuous, compactly supported solution which has independent lattice translates, then the joint spectral radius of certain matrices restricted to an appropriate subspace is strictly less than one. © 2000 SPIE--The International Society for Optical Engineering.
| Documento: | Artículo |
| Título: | Necessary conditions for the existence of multivariate multiscaling functions |
| Autor: | Cabrelli, C.A.; Heil, C.; Molter, U.M. |
| Filiación: | Departamento de Matemática, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, United States |
| Palabras clave: | Joint spectral radius; Multiresolution analysis; Multiwavelets; Refinement equations; Tiles; Wavelets; Algorithms; Boundary conditions; Convergence of numerical methods; Fractals; Function evaluation; Matrix algebra; Set theory; Theorem proving; Vectors; Joint spectral radius; Multiresolution analysis; Multivariate multiscaling functions; Refinement equations; Tiles; Wavelet transforms |
| Año: | 2000 |
| Volumen: | 4119 |
| Número: | 1 |
| Página de inicio: | 395 |
| Página de fin: | 406 |
| DOI: | http://dx.doi.org/10.1117/12.408625 |
| Título revista: | Proceedings of SPIE - The International Society for Optical Engineering |
| Título revista abreviado: | Proc SPIE Int Soc Opt Eng |
| ISSN: | 0277786X |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0277786X_v4119_n1_p395_Cabrelli |
