The knowledge of the nullspace and its size of some structured matrices, like Hankel and Toeplitz matrices, is important in many applications arising in system theory. In this paper we describe an algorithm to compute the kernel of Toeplitz and Hankel matrices based on the generalized Schur algorithm.

second language acquisition (sla) always happens when the learners live and have contact with the native speakers of a second language. although this study investigates learning english by ten native children of farsi, the authors try to simulate the second language acquisition environment. the research deals with the initial state and further development in the child second language learning o...

In this paper we consider a Hankel determinant formula for generic solutions of the Painlevé II equation. We show that the generating functions for the entries of the Hankel determinants are related to the asymptotic solution at infinity of the linear problem of which the Painlevé II equation describes the isomonodromic deformations.

In this paper we completely characterize compact Toeplitz operators on the harmonic Bergman space. By using this result we establish the short exact sequences associated with the Toeplitz algebra and the Hankel algebra. We show that the Fredholm index of each Fredholm operator in the Toeplitz algebra or the Hankel algebra is zero.  2002 Elsevier Science (USA). All rights reserved.

We show that a big Hankel operator on the standard Hardy space of the polydisk D, n > 1, cannot be compact unless it is the zero operator. We also show that this result can be generalized to certain Hankel operators defined on Hardy-Sobolev spaces of the polydisk.

Connections between Hankel transforms of different order for L-functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different order. Consequences for Hankel multipliers are exhibited and implications for radial Fourier multipliers on Euclidean spaces of different dimensions indicated.

A class of matrices is studied that could be considered as Hankel matrices with respect to a system of orthogonal polynomials. It is shown that they have similar properties like classical Hankel matrices. Main attention is paid to the construction of fast and superfast algorithms. The main tool is the fact that these matrices are matrix representation of multiplication operators.

In this present paper, we define a new operator in conjugation with the basic (or q-) calculus. We then make use of newly defined and class analytic bi-univalent functions associated q-derivative operator. Furthermore, find initial Taylor–Maclaurin coefficients for these function classes functions. also show that bounds are sharp. The sharp second Hankel determinant is given class.