In this paper it is investigated how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs). Therefore it is useful to extend the known method of matrix representation by using these sequences instead of ONBs for these application areas. We will give ba...

The main purpose of this paper is providing a systematic study and classification of non-scalar kernels for Reproducing Kernel Hilbert Spaces (RKHS), to be used in the analysis of deformation in shape spaces endowed with metrics induced by the action of groups of diffeomorphisms. After providing an introduction to matrix-valued kernels and their relevant differential properties, we explore exte...

Abstract. We develop a new asymptotic method for the analysis of matrix Riemann-Hilbert problems. Our method is a generalization of the steepest descent method first proposed by Deift and Zhou; however our method systematically handles jump matrices that need not be analytic. The essential technique is to introduce nonanalytic extensions of certain functions appearing in the jump matrix, and to...

In this work we will investigate how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames and Riesz bases as an extension of the known method of matrix representation by ONBs. We will give basic definitions of the functions connecting infinite matrices defining bounded operators on l and operators onH. We will show some structural results and give some...

The core inverse of matrix is generalized inverse which is in some sense in-between the group and Moore–Penrose inverse. In this paper a generalization of core inverse and core partial order to Hilbert space operator case is presented. Some properties are generalized and some new ones are proved. Connections with other generalized inverses are obtained. The useful matrix representations of oper...

In this study, we investigate the norm of difference operator on some sequence spaces such as Hilbert and Cesaro matrix domains. Therefore present study is a complement for those results obtained in [1].

I. Abstract The random matrix ensembles (RME) of Hamiltonian matrices, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applicable to following quantum statistical systems: nuclear systems, molecular systems, condensed phase systems, disordered systems, and two-dimensional electron systems (WignerDyson electrostatic analogy). A family of quantu...

In these notes we solve a class of Riemann-Hilbert (inverse monodromy) problems with an arbitrary quasi-permutation monodromy group. The solution is given in terms of Szegö kernel on the underlying Riemann surface. In particular, our construction provides a new class of solutions of the Schlesinger system. We present some results on explicit calculation of the corresponding tau-function, and de...

The objective of this paper is to develop algorithms for efficient and fast implementation in a multilayered mode of signal-processing tasks such as convolution, correlation, matrix multiplication, Fourier transformation, Hilbert transformation, etc., using structures built out of a large number of simple cells. Some of these designs are essentially conceptual, while others, such as the ones fo...

The purpose of this note is to show that any order isomorphism between noncommutative L2-spaces associated with von Neumann algebras is decomposed into a sum of a completely positive map and a completely copositive map. The result is an L2 version of a theorem of Kadison for a Jordan isomorphism on operator algebras.