Riesz multiresolution analysis on locally compact abelian groups: construction and exceptions (Q6060257)

The authors define the concept of a Riesz multiresolution analysis on a locally compact abelian group \(G\) equipped with a lattice subgroup, \(\Gamma\), and a compatible dilative automorphism, \(\alpha\). The examples given are the positive real numbers under multiplication with squaring as the dilative automorphism and the additive reals with dilation by~3. They also point out some examples of locally compact abelian groups where no dilative automorphism could exist.