The q-derivative and Hohlov operators have seen much use in recent years. First, numerous well-known principles of the operator are highlighted explained this research. We then build a novel subclass analytic bi-univalent functions using certain q-Chebyshev polynomials. A number coefficient bounds, as well Fekete–Szegö inequalities second Hankel determinant provided for these newly specified fu...

We show that the Hankel determinants of a generalized Catalan sequence satisfy the equations of the elliptic sequence. As a consequence, the coordinates of the multiples of an arbitrary point on the elliptic curve are expressed by the Hankel determinants. PACS numbers: 02.30.Ik, 02.30.Gp, 02.30.Lt

Transformations Preserving the Hankel Transform Christopher French Department of Mathematics and Statistics Grinnell College Grinnell, IA 50112 USA [email protected] Abstract We classify all polynomial transformations of integer sequences which preserve the Hankel transform, thus generalizing examples due to Layman and Spivey & Steil. We also show that such transformations form a group ...

l h e problem of approximating a high order controller by a low order one is tackled with the aid of a frequency-weighted Hankel norm approximation procedure. Bounds are obtained which weight those arising in the unweighted Hankel norm approximation procedure by a factor depending solely on the weighting function. Keywards. Controllers; approximation theory; controller reduction; system order r...

We study a constructive method of rational approximation of analytic functions based on ideas of the theory of Hankel operators. Some properties of the corresponding Hankel operator are investigated. We also consider questions related to the convergence of rational approximants. Analogues of Montessus de Ballore’s and Gonchars’s theorems on the convergence of rows of Padé approximants are proved.

The relationship between the mode content and the fractional Fourier and fractional Hankel transforms of a function is established. It is shown that the Laguerre-Gauss spectrum of a rotationally symmetric wave front can be determined from the wave front's fractional Hankel transforms taken at the optical axis.

We apply and extend some well known and some recent techniques from algebraic residue theory in order to relate to each other two major subjects of algebraic and numerical computing that is computations with structured matrices and solving a system of polynomial equations In the rst part of our paper we extend the Toeplitz and Hankel structures of matrices and some of their known properties to ...

We introduce a new approach to Nehari’s problem. This approach is based on some kind of fixed point theorem and allows us to obtain some useful generalizations of Nehari’s and Adamyan – Arov – Krein (AAK) theorems. Among those generalizations: descriptions of Hankel operators in weighted 2 spaces; descriptions of Hankel operators from Dirichlet type spaces to weighted Bergman spaces; commutant ...