We extend recent results by Pisier on K-subcouples, i.e. subcouples of an interpolation couple that preserve the K-functional (up to constants) and corresponding notions for quotient couples. Examples include interpolation (in the pointwise sense) and a reinter-pretation of the Adamyan-Arov-Krein theorem for Hankel operators.

In this article, we present various new results on Cauchy tensors and Hankel tensors. We first introduce the concept of generalized Cauchy tensors which extends Cauchy tensors in the current literature, and provide several conditions characterizing positive semi-definiteness of generalized Cauchy tensors with nonzero entries. Furthermore, we prove that all even order generalized Cauchy tensorsw...

The purpose of this paper is to represent the integral Hankel transform as a series. If one uses Bspline wavelet this series is a linear combination of the hypergeometrical functions. Numerical evaluation of the test function with known analytical Hankel transform of the null kind illustrates the proposed results. Key-Words: the Hankel transform, hypergeometrical function, B-spline wavelet.

One of the most important problems in study geometric function theory is knowing how to obtain sharp bounds coefficients that appear Taylor–Maclaurin series univalent functions. In present investigation, our aim calculate some estimates involving for family convex functions with respect symmetric points and associated a hyperbolic tangent function. These include first four initial coefficients,...

We use the Paley–Wiener theorem for the Fourier and Hankel transforms to compare Fourier and Hankel Sampling.

New algorithms for Toeplitz and Toeplitz-plus-Hankel are presented that are in the spirit of the “split” algorithms of Delsarte/Genin. It is shown that the split algorithms are related to ZW-factorizations like the classical algorithms are related to LU-factorizations. Special attention is paid to skewsymmetric Toeplitz, centrosymmetric Toeplitz-plus-Hankel and general Toeplitz-plus-Hankel matr...

Bounds for the second Hankel determinant of certain bi-univalent functions Halit ORHAN, Nanjundan MAGESH, Jagadeesan YAMINI Department of Mathematics Faculty of Science, Atatürk University 25240 Erzurum, Turkey. Post-Graduate and Research Department of Mathematics, Government Arts College for Men, Krishnagiri 635001, Tamilnadu, India. Department of Mathematics, Govt First Grade College Vijayana...

Postnicov [22], in 2003, proposed an algorithm to compute the Hankel transforms of order zero and one by using Haar wavelets. But the proposed method faced problems in the evaluation of zero order Hankel transform. The purpose of this paper is to overcome this problem and obtain an efficient algorithm for evaluating Hankel transform of order zero by using rationalized Haar wavelets. Exact analy...

We investigate tournaments with a specified score vector having additional structure: loopy tournaments in which loops are allowed, Hankel tournaments which are tournaments symmetric about the Hankel diagonal (the anti-diagonal), and combinatorially skew-Hankel tournaments which are skew-symmetric about the Hankel diagonal. In each case, we obtain necessary and sufficient conditions for existen...

Ehrenborg gave a combinatorial proof of Radoux’s theorem which states that the determinant of the (n + 1)× (n + 1) dimensional Hankel matrix of exponential polynomials is x ∏n i=0 i!. This proof also shows the result that the (n + 1) × (n + 1) Hankel matrix of factorial numbers is ∏n k=1(k!) . We observe that two polynomial generalizations of factorial numbers also have interesting determinant ...