The purpose of this paper is to present an algorithm for evaluating Hankel transform of the null and the first kind to the series of the Bessel function for Hankel transform of the first kind and Bessel and Struve function for Hankel transform of the null kind multiplied to the wavelet coefficients of the input function. It is both the exact analytical representation and the base for effective ...

In the present paper, we aimed to discuss certain coefficient-related problems for inverse functions associated with a bounded turning class subordinated exponential function. We calculated bounds of some initial coefficients, Fekete–Szegö-type inequality, and estimation Hankel determinants second third order. All these were proven be sharp.

We extend to multilinear Hankel operators a result on the regularity of truncations of Hankel operators. We prove and use a continuity property on the bilinear Hilbert transforms on product of Lipschitz spaces and Hardy spaces. In this note, we want to extend to multilinear Hankel operators a result obtained by [BB] on the boundedness properties of truncation acting on bounded Hankel infinite m...

Bounded, semi-infinite Hankel matrices of finite rank over the space l of square-summable sequences occur frequently in classical analysis and engineering applications. The notion of finite rank often appears under different contexts and the literature is diverse. The first part of this paper reviews some elegant, classic criteria and establish connections among the various characterizations of...

We present different stability estimates for the Jacobi inverse eigenvalue problem. First, we give upper bounds expressed in terms of quadrature data and not having weights in denominators. The technique of orthonormal polynomials and integral representation of Hankel determinants is used. Our bounds exhibit only polynomial growth in the problem’s dimension (see [4]). It has been shown that the...

where V 2 is the two-dimensional Laplace operator and k is the wavenumber of the radiation field. The function Vstands for a typical component of the electric or magnetic field. In cylindrical coordinates, the basic solutions of the Helmholtz equation are of the form Hn (kr ) exp (int~), where Hn is the Hankel function of integer order n while r and ot are a radial and an angular coordinate, re...

Hankel matrices consisting of Catalan numbers have been analyzed by various authors. DesainteCatherine and Viennot found their determinant to be ∏ 1≤i≤j≤k i+j+2n i+j and related them to the Bender Knuth conjecture. The similar determinant formula ∏ 1≤i≤j≤k i+j−1+2n i+j−1 can be shown to hold for Hankel matrices whose entries are successive middle binomial coefficients (2m+1 m ) . Generalizing t...

In our previous works “Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants” (by M.Ishikawa, H. Tagawa and J. Zeng, J. Combin. Theory Ser. A, 120, 2013, 1263–1284) we have proposed several ways to evaluate certain Catalan-Hankel Pffafians and also formulated several conjectures. In this work we propose a new approach to compute these Catalan-Hankel Pffafians using Sel...

A set of new formulae for the inverse of a block Hankel (or block Toeplitz) matrix is given. The formulae are expressed in terms of certain matrix Pad6 forms, which approximate a matrix power series associated with the block Hankel matrix. By using Frobenius-type identities between certain matrix Pad6 forms, the inversion formulae are shown to generalize the formulae of Gohberg-Heinig and, in t...