This paper surveys the progress made on pairwise orthogonal wavelet frames and comments on the construction methods. There are a few known constructions based on the unitary extension principle, a paraunitary matrix and a given modulation matrix. A polyphase matrix based construction method has been presented which satisfies the condition of unitary extension principle yielding pairwise orthogo...

This is a review of the Riemann-Hilbert approach to the large N asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to the large N asymptotics of orthogonal polynomials and its applications to the problem of universality in random matrix models, the double scaling limits, the lar...

This is a review of the Riemann-Hilbert approach to the large N asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to the large N asymptotics of orthogonal polynomials and its applications to the problem of universality in random matrix models, the double scaling limits, the lar...

A system of multivariate orthogonal polynomials satisfies a matrix equation which plays the role of a three-term relation of the orthogonal polynomial of one variable. However, unlike the case of one variable, there does not exist a second solution of this matrix equation that is linearly independent to the orthogonal polynomials. In particular, there is no analogy of the associated polynomials...

We consider the following problem: When do alternate eigenvalues taken from a matrix ensemble themselves form a matrix ensemble? More precisely, we classify all weight functions for which alternate eigenvalues from the corresponding orthogonal ensemble form a symplectic ensemble, and similarly classify those weights for which alternate eigenvalues from a union of two orthogonal ensembles forms ...

We study the moment space corresponding to matrix measures on the unit circle. Moment points are characterized by non-negative definiteness of block Toeplitz matrices. This characterization is used to derive an explicit representation of orthogonal polynomials with respect to matrix measures on the unit circle and to present a geometric definition of canonical moments. It is demonstrated that t...

We discuss the universality of the l1 recovery threshold in compressed sensing. Previous studies in the fields of statistical mechanics and random matrix integration have shown that l1 recovery under a random matrix with orthogonal symmetry has a universal threshold. This indicates that the threshold of l1 recovery under a non-orthogonal random matrix differs from the universal one. Taking this...

We discuss the universality of the l1 recovery threshold in compressed sensing. Previous studies in the fields of statistical mechanics and random matrix integration have shown that l1 recovery under a random matrix with orthogonal symmetry has a universal threshold. This indicates that the threshold of l1 recovery under a non-orthogonal random matrix differs from the universal one. Taking this...