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Publications Influence

Frames, bases, and group representations

- Deguang Han, D. Larson
- Mathematics
- 2000

Introduction Basic theory for frames Complementary frames and disjointness Frame vectors for unitary systems Gabor type unitary systems Frame wavelets, super-wavelets and frame sets Frame… Expand

471 29- PDF

Frames for Undergraduates

- Deguang Han
- Mathematics
- 5 December 2007

Introduction Linear algebra review Finite-dimensional operator theory Introduction to finite frames Frames in $\mathbb{R}^2$ The dilation property of frames Dual and orthogonal frames Frame operator… Expand

145 8- PDF

FRAMES FOR BANACH SPACES

- P. Casazza, Deguang Han, D. Larson
- 1977

We use several fundamental results which characterize frames for a Hilbert space to give natural generalizations of Hilbert space frames to general Banach spaces. However, we will see that all of… Expand

109 8- PDF

On multiresolution analysis (MRA) wavelets in ℝn

- Q. Gu, Deguang Han
- Mathematics
- 1 July 2000

We prove that for any expansive n×n integral matrix A with |det A|=2, there exist A-dilation minimally supported frequency (MSF) wavelets that are associated with a multiresolution analysis (MRA).… Expand

52 8

Lattice tiling and the Weyl—Heisenberg frames

- Deguang Han, Y. Wang
- Mathematics
- 1 November 2001

Abstract. Let {\cal L} and {\cal K} be two full rank lattices in
$ {\Bbb R}^d $. We prove that if
$ {\rm v}({\cal L} ) = {\rm v}({\cal K}) $, i.e. they have the same volume, then there exists a… Expand

81 6- PDF

Frames Associated with Measurable Spaces

- J. Gabardo, Deguang Han
- Mathematics, Computer Science
- Adv. Comput. Math.
- 1 February 2003

TLDR

122 6

Optimal dual frames for erasures

- Jerry Lopez, Deguang Han
- Mathematics
- 2010

For any given frame (for the purpose of encoding) in a finite dimensional Hilbert space, we investigate its dual frames that are optimal for erasures (for the purpose of decoding). We show that in… Expand

62 5- PDF

The existence of subspace wavelet sets

- X. Dai, Y. Diao, Q. Gu, Deguang Han
- Mathematics
- 1 June 2003

Let H be a reducing subspace of L2(Rd), that is, a closed subspace of L2(Rd) with the property that f(Amt - l) ∈ H for any f ∈ H, m ∈ Z and l ∈ Zd, where A is a d × d expansive matrix. It is known… Expand

36 4- PDF

FRAME REPRESENTATIONS FOR GROUP-LIKE UNITARY OPERATOR SYSTEMS

- J. Gabardo, Deguang Han
- Mathematics
- 2003

Communicated by S Str˘atil˘a Abstract. A group-like unitary system U is a set of unitary operators such that the group generated by the system is contained in TU, where T denotes the unit circle.… Expand

66 4- PDF

The existence of Gabor bases and frames

- Deguang Han, Y. Wang
- Mathematics
- 2004

For an arbitrary full rank lattice Λ in R and a function g ∈ L(R) the Gabor (or Weyl-Heisenberg) system is G(Λ, g) := {eg(x − κ) ̨ ̨ (κ, `) ∈ Λ}. It is well-known that a necessary condition for G(Λ,… Expand

23 4- PDF