As a rapidly growing, multidisciplinary field of mathematics, wavelet theory provides the
major mathematical multiscale representation for analyzing functions/data and has …

We study nonstationary frames of matrix-valued Gabor systems and wavelet systems in the
matrix-valued function space L 2 (ℝ, ℂ l× l). First, we show that a diagonal matrix-valued …

We characterize scaling functions of nonstationary matrix-valued multiresolution analysis in
the matrix-valued function space L 2 (R, C l× l), l is a natural number. This is inspired by the …

Gabor frames have interested many mathematicians and physicists due to their potential
applications in time-frequency analysis, in particular, signal processing. A Gabor system is a …

We study approximation properties of multi-resolution analyses in the context of matrix-
valued function spaces. Here, we generalize the notions of approximation order and density …

In this paper, we study multivariate Gabor frames in matrix-valued signal spaces over locally
compact abelian (LCA) groups, where the lower frame condition depends on a bounded …

In a vector-valued nonuniform multiresolution analysis (VNUMRA, in short), the
corresponding translation set may not be a subgroup of R, but a spectrum associated with …

We study frame properties of a matrix-valued wave packet system in the matrix-valued
function space L 2 (ℝ d, ℂ s× r) L^2(R^d,C^s*r), where the lower frame condition is …

The image of a given orthonormal basis for a separable Hilbert space $\mathcal {H} $ under
a bijective, bounded, and linear operator acting on $\mathcal {H} $ is called a Riesz basis of …

Dual frames are generalized Riesz bases which have potential applications in signal
processing. In this paper, the construction of dual frames of matrix-valued wave packet …