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The aim of this paper is to construct sup-exponentially localized kernels and frames in the context of classical orthogonal expansions, namely, expansions in Jacobi polynomials, spherical harmonics, orthogonal polynomials on the ball and simplex, and Hermite and Laguerre functions.

We present a characterization of the approximation errors of the Post-Widder and the Gamma operators in Lp[0, ∞), 1 ≤ p ≤ ∞, with a weight x γ for any real γ. Two types of characteristics are used – weighted K-functionals of the approximated function itself and the classical fixed step moduli of smoothness taken on a simple modification of it.

- Kamen G. Ivanov, Pencho Petrushev
- Adv. Comput. Math.
- 2015

A method for fast evaluation of spherical polynomials (band-limited functions) at many scattered points on the unit 2-d sphere is presented. The method relies on the sub-exponential localization of the father needlet kernels and their compatibility with spherical harmonics. It is fast, local, memory efficient, numerically stable and with guaranteed… (More)

Article history: Received 27 September 2013 Received in revised form 5 May 2014 Accepted 13 May 2014 Available online xxxx Communicated by W.R. Madych MSC: 65T99 42C10 33C55 65D15

- Borislav R. Draganov, Kamen G. Ivanov
- Journal of Approximation Theory
- 2007

We present a characterization of the approximation errors of the PostWidder and the Gamma operators in Lp(0,∞), 1 ≤ p ≤ ∞, with a weight x for any real γ. Two types of characteristics are used – weighted Kfunctionals of the approximated function itself and the classical fixed step moduli of smoothness taken on a simple modification of it. AMS… (More)

- V D Beliakov, K G Ivanov, N G Bundzen, P S Tentser, Iu D Maliarenko
- Trudy Instituta imeni Pastera
- 1976

- K. G. Ivanov, P. E. Parvanov
- 2010

The uniform weighted approximation errors of Baskakov-type operators are characterized for weights of the form ( x 1 + x )γ0 (1 + x)∞ for γ0, γ∞ ∈ [−1, 0]. Direct and strong converse theorems are proved in terms of the weighted K-functional. AMS classification: 41A36, 41A17, 41A25, 41A27.

- K G Ivanov, V D Beliakov, M I Ishkil'din, Iu D Maliarenko
- Trudy Instituta imeni Pastera
- 1976

For the infinite triangular arrays of points whose rows consist of (i) the nth roots of unity, (ii) the extrema of Chebyshev polynomials Tn(x) on [—1,1], and (iii) the zeros of Tn(x), we consider the corresponding sequences of divided difference functionals {In}f in the successive rows of these arrays. We investigate the totality of such functionals as well… (More)

- V D BELIAKOV, K G IVANOV, A A IL'CHENKO
- Voenno-medit︠s︡inskiĭ zhurnal
- 1959