where φ :Rn → C and φt(x)= t−nφ(x/t), t > 0. For conditions of validity of identity (1.1), we may refer to [3]. Hankel convolution introduced by Hirschman Jr. [5] related to the Hankel transform was studied at length by Cholewinski [1] and Haimo [4]. Its distributional theory was developed byMarrero and Betancor [6]. Pathak and Pandey [8] used Hankel convolution in their study of pseudodifferen...

In this paper, we give an explicit expression for the Hankel determinants for a sequence satisfying a three-term recurrence relation. Our method of evaluation is based on the theory of orthogonal polynomials. In particular, we analyze the linear functional associated with such a sequence.

Anti-circulant tensors have applications in exponential data fitting. They are special Hankel tensors. In this paper, we extend the definition of anti-circulant tensors to generalized anticirculant tensors by introducing a circulant index r such that the entries of the generating vector of a Hankel tensor are circulant with module r. In the special case when r=n, where n is the dimension of the...

‎The subject of this paper is the solution of the Fredholm integral equation with Toeplitz, Hankel and the Toeplitz plus Hankel kernel. The mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.

This letter studies identification problems of model orders using the Hankel matrix of impulse responses of a system and presents two order identificationmethods: one is based on the singularities or ratios of the Hankel matrix determinants and the other is based on the singular value decomposition of the Hankel matrix. A numerical example verifies the proposed methods. © 2011 Elsevier Ltd. All...

In this paper, we consider the class of strongly bi-close-to-convex functions order ? and ?. We obtain an upper bound estimate for second Hankel determinant belonging to these classes. The results in article improve some earlier result obtained bi-convex functions.

The objective of this paper is to obtain an upper bound to the second Hankel determinant |ap+1ap+3 − ap+2| for p-valent starlike and convex functions of order α, using Toeplitz determinants. AMS Mathematics Subject Classification (2010): 30C45, 30C50

We define a generalization of the Stirling numbers of the second kind, which depends on two parameters. The matrices of integers that result are exponential Riordan arrays. We explore links to orthogonal polynomials by studying the production matrices of these Riordan arrays. Generalized Bell numbers are also defined, again depending on two parameters, and we determine the Hankel transform of t...

The Hankel transform for sequences (defined below) has attracted an increasing amount of attention in recent years. The paper [4] situated its study within the mainstream of research into integer sequences, while papers such as [2] hinted at how the study of certain Hankel transforms can lead to results concerning classical sequences. That paper exploited a link between continued fractions and ...

9.1.1 The Optimization Setup Let G = G(s) be a matrix-valued function bounded on the jθ-axis. The task of Hankel ˆ optimal model reduction of G calls for finding a stable LTI system G of order less than a given positive integer m, such that the Hankel norm ∞�∞H of the difference � = G − Ĝ is minimal. Remember that Hankel norm of an LTI system with transfer matrix � = �(s), input w, and output v...