Abstract
This paper is devoted to the construction of wavelet (or coherent state) systems arising from the action of certain semidirect products G=Rk⋊H on L2(Rk). For this purpose previous results which guarantee the existence of inversion formulas are applied to the special case where H is Abelian. The questions of systematic construction and conjugacy of such groups are completely resolved by setting up a correspondence to unit groups of commutative associative algebras. As an application the numbers of conjugacy classes of possible Abelian groups are computed for k=2,3,4. For k⩾7, there are uncountably many conjugacy classes. We then compute the admissibility conditions belonging to Abelian groups. The final section contains a characterization of Abelian matrix groups acting ergodically on some subset of Rk. This result ensures that the approach via associative algebras yields all possible groups.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.