Deguang Han

Frames for Undergraduates

Introduction Linear algebra review Finite-dimensional operator theory Introduction to finite frames Frames in

Frames Associated with Measurable Spaces

\mathbb{R}^2

Lattice tiling and the Weyl-Heisenberg frames

The dilation property of frames Dual and orthogonal frames Frame operator decompositions Harmonic and group frames Sampling theory Student presentations Anecdotes on frame theory projects by undergraduates Bibliography List of symbols Index.

Balian–Low phenomenon for subspace Gabor frames

We present two results dealing with dilation and perturbation properties of general frames, which generalize the works of several authors in the theory of discrete frames. We also study the representing measures associated with frames. In particular, we give a necessary and sufficient condition for a representing measure to be an extreme point of the set of representing measures and show how it can be used in some concrete examples.

Subspace Weyl-Heisenberg frames

Abstract. Let {\cal L} and {\cal K} be two full rank lattices in

The Balian–Low theorem for symplectic lattices in higher dimensions

{\Bbb R}^d

Frame representations and Parseval duals with applications to Gabor frames

. We prove that if

Sampling Expansions in Reproducing Kernel Hilbert and Banach Spaces

{\rm v}({\cal L} ) = {\rm v}({\cal K})

Wandering vector multipliers for unitary groups

, i.e. they have the same volume, then there exists a measurable set

The existence of subspace wavelet sets

\Omega