Gerlind Plonka
Necessary and sufficient conditions for orthonormality of scaling vectors
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

42C15 Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions

Abstract: The paper studies neccessary and sufficient orthonormality conditions
for a scaling vector in terms of its two-scale symbol and its
corresponding transfer operator. In particular, it is shown, that the
conditions of Hogan [10] for the two-scale symbol and the criteria of
Shen [21] for the transfer operator are equivalent.
Keywords: scaling vectors, two-scale symbol, transfer operator, L^2-stability, orthonormality