Results 11 to 20 of about 52 (52)
Strict positive definiteness on spheres via disk polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 12, Page 715-724, 2002., 2002 We characterize complex strictly positive definite functions on spheres in two cases, the unit sphere of ℂq, q ≥ 3, and the unit sphere of the complex ℓ2. The results depend upon the Fourier‐like expansion of the functions in terms of disk polynomials and, among other things, they enlarge the classes of strictly positive definite functions on real ...
V. A. Menegatto, A. P. Peron
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Integral representations for Padé‐type operators
Journal of Applied Mathematics, Volume 2, Issue 2, Page 51-69, 2002., 2002 The main purpose of this paper is to consider an explicit form of the Padé‐type operators. To do so, we consider the representation of Padé‐type approximants to the Fourier series of the harmonic functions in the open disk and of the L p‐functions on the circle by means of integral formulas, and, then we define the corresponding Padé‐type operators. We
Nicholas J. Daras
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Stečkin inequalities for summability methods
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 1, Page 93-100, 1997., 1995 Stečkin proved an inequality on Fejér means of Fourier series He said, “Proving similar inequality for other summability method is an interesting problem.” We generalize Stečkin′s inequality and give various applications to summability methods.
Jia-Ding Cao
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The Paley‐Wiener‐Levinson theorem revisited
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 2, Page 229-234, 1997., 1995 In this paper a new proof of the Paley‐Wiener‐Levinson theorem is presented. This proof is based upon the isometry between the Paley‐Wiener space and that of the square‐integrable functions in [−π, π], on one hand, and a Titchmarsh′s theorem which allows recovering bandlimited, entire functions from their zeros, on the other hand.
A. G. García
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A generalization of Hermite interpolation
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 719-725, 1997., 1996 We introduce a new interpolation at Chebyshev nodes.
Xie-Hua Sun, Tingfan Xie
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On approximation of functions and their derivatives by quasi‐Hermite interpolation
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 2, Page 279-286, 1996., 1994 In this paper, we consider the simultaneous approximation of the derivatives of the functions by the corresponding derivatives of quasi‐Hermite interpolation based on the zeros of (1 − x2)pn(x) (where pn(x)is a Legendre polynomial). The corresponding approximation degrees are given. It is shown that this matrix of nodes is almost optimal.
G. Min
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International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 2, Page 209-216, 1994., 1993 We continue the investigation initiated by Mastroianni and Szabados on question whether Jackson′s order of approximation can be attained by Lagrange interpolation for a wide class of functions. Improving a recent result of Mastroianni and Szabados, we show that for a subclass of C1 functions the local order of approximation given by Lagrange ...
Xin Li
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On approximation in the Lp‐norm by Hermit interpolation
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 1, Page 35-39, 1992., 1991 Lp‐approximation by the Hermite interpolation based on the zeros of the Tchebycheff polynomials of the first kind is considered. The corresponding result of Varma and Prasad [1] is generalized and perfected.
Min Guohua
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Equiconvergence of some sequences of rational functions
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 2, Page 221-228, 1992., 1992 The phenomenon of equiconvergence was first observed by Walsh for two sequences of polynomial interpolants to a class of functions. Here we obtain analogues of Yuanren′s results for Walsh equiconvergence using rational functions as in Saff and Sharma. We extend this to Hermite interpolation and an earlier result of [1] is improved and corrected.
M. A. Bokhari, A. Sharma
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Interpolation of natural cubic spline
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 2, Page 229-234, 1992., 1990 From the result in [1] it follows that there is a unique quadratic spline which bounds the same area as that of the function. The matching of the area for the cubic spline does not follow from the corresponding result proved in [2]. We obtain cubic splines which preserve the area of the function.
Arun Kumar, L. K. Govil
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