*PN* 95/22 TI eng: Construction of Multi-Scaling Functions with Approximation and Symmetry dt: Konstruktion von Multiskalierungsfunktionen mit Approximationsordnung und Symmetrie AU Plonka, Gerlind and Strela, Vasily SO Preprint 95/22, ISSN 0948-1028 LA englisch AB This paper presents a new and efficient way to create multi-scaling functions with given approximation order, regularity, symmetry and short support. Previous techniques were operating in the time domain and required the solution of large systems of nonlinear equations. By switching to the frequency domain and employing the latest results of the multiwavelet theory we were able to elaborate a simple and efficient method of construction of multi-scaling functions. Our algorithm is based on a recently found factorization of the refinement mask through the two-scale similarity transform (TST). Theoretical results and new examples are presented. CC 41A25, 42A38, 39B62 UT Approximation order, symmetry, multi-scaling functions, multiwavelets