My general research area is Harmonic Analysis, Wavelets, and Frames.
My research areas are:
non-isotropic function spaces such as: anisotropic Hardy, Besov, and Triebel-Lizorkin spaces and their wavelet decompositions,
construction and non-existence results for wavelets with good regularity properties associated with arbitrary dilations,
L2-theory of wavelets and frame wavelets: characterization theorems, quasi-affine systems, the wavelet dimension function, canonical and alternate duals of frame wavelets, connectivity results, Riesz wavelets,
the structure of shift-invariant spaces in L2(Rn): range, dimension, and spectral functions, refinable spaces, generalized multi-resolution analysis,
Gabor (Weyl-Heisenberg) systems: the structure of shift-modulation invariant spaces, Gabor frame sequences,
weighted norm inequalities: theory of matrix-valued weights generalizing scalar Muckenhoupt Ap weights.
You can also look at my old research interests circa 2000.
Last updated: January 4, 2007.