The object of this present paper is to study Toeplitz operators and Hankel operators on the Hardy space of the unit sphere S in C through the generalized area integral of harmonic functions on the unit ball B in C. In particular we consider the question of when the product of two Toeplitz operators is a compact perturbation of a Toeplitz operator. It follows from a theorem in [DJ] that T,T can ...

In [P90] we proposed to employ Vandermonde and Hankel multipliers to transform into each other the matrix structures of Toeplitz, Hankel, Vandermonde and Cauchy types as a means of extending any successful algorithm for the inversion of matrices having one of these structures to inverting the matrices with the structures of the three other types. Surprising power of this approach has been demon...

The structured total least squares estimator, defined via a constrained optimization problem, is a generalization of the total least squares estimator when the data matrix and the applied correction satisfy given structural constraints. In the paper, an affine structure with additional assumptions is considered. In particular, Toeplitz and Hankel structured, noise free and unstructured blocks a...

Abstract The paper is devoted to the study of compactness Hankel operators acting between distinct Hardy spaces generated by Banach function lattices. We prove an analogue Hartman’s theorem characterizing compact in terms properties their symbols. As a byproduct we give estimation essential norm such operators. Furthermore, commutators and semicommutators Toeplitz for unbounded symbols discussed.

In the second part of this paper we study condition numbers with respect to componentwise perturbations in the input data for linear systems and for matrix inversion, and the distance to the nearest singular matrix. The structures under investigation are linear structures, namely symmetric, persymmetric, skewsymmetric, symmetric Toeplitz, general Toeplitz, circulant, Hankel, and persymmetric Ha...

Orthogonal systems in L2(ℝ), once implemented spectral methods, enjoy a number of important advantages if their differentiation matrix is skew-symmetric and highly structured. Such systems, where the skew-symmetric, tridiagonal, irreducible, have been recently fully characterised. In this paper we go step further, imposing extra requirement fast computation: specifically, that first N coefficie...

In [P90] we proposed to employ Vandermonde and Hankel multipliers to transform into each other the matrix structures of Toeplitz, Hankel, Vandermonde and Cauchy types as a means of extending any successful algorithm for the inversion of matrices having one of these structures to inverting the matrices with the structures of the three other types. Surprising power of this approach has been demon...

The estimation of the frequencies of sinusoids in noise is a very common problem. This paper addresses the estimation of sinusoids in a low SNR environment. This sinusoidal frequency estimation problem can be used to nd the carrier frequencies and baud rates of communication waveforms after some appropriate nonlinearity. If the underlying signal model is sinusoids in white Gaussian noise and we...