arXiv subjects

Deguang Han

Publications and source records attributed to Deguang Han.

38 records · Page 3Linked to original sources

arXiv2007

Orthonormal dilations of Parseval wavelets

We prove that any Parseval wavelet frame is the projection of an orthonormal wavelet basis for a representation of the Baumslag-Solitar group $$BS(1,2)=< u,t | utu^{-1}=t^2>.$$ We give a precise description of this representation in some special cases, and show that for wavelet sets, it is related to symbolic dynamics. We show that the structure of the representation depends on the analysis of certain finite orbits for the associated symbolic dynamics. We give concrete examples of Parseval wavelets for which we compute the orthonormal dilations in detail; we show that there are examples of Parseval wavelet sets which have infinitely many non-isomorphic orthonormal dilations.

math.FA↗

arXiv2006

Structured Parseval Frames in Hilbert $C^*$-modules

We investigate the structured frames for Hilbert $C^{*}$-modules. In the case that the underlying $C^{*}$-algebra is a commutative $W^*$-algebra, we prove that the set of the Parseval frame generators for a unitary operator group can be parameterized by the set of all the unitary operators in the double commutant of the group. Similar result holds for the set of all the general frame generators where the unitary operators are replaced by invertible and adjointable operators. Consequently, the set of all the Parseval frame generators is path-connected. We also obtain the existence and uniqueness results for the best Parseval multi-frame approximations for multi-frame generators of unitary operator groups on Hilbert $C^*$-modules when the underlying $C^{*}$-algebra is commutative.

math.FA↗