Research

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 A_p weights.

You can also look at my old research interests circa 2000.

Last updated: January 4, 2007.