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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 polynomi-als on the ball and simplex, and Hermite and Laguerre functions.

Rapidly decaying kernels and frames (needlets) in the context of tensor product Jacobi polynomials are developed based on several constructions of multivariate C ∞ cutoff functions. These tools are further employed to the development of the theory of weighted Triebel-Lizorkin and Besov spaces on [−1, 1] d. It is also shown how kernels induced by cross… (More)

a r t i c l e i n f o a b s t r a c t An iterative algorithm for stable and accurate reconstruction of band-limited functions from irregular samples on the unit 2-d sphere is developed. Geometric rate of convergence in the uniform norm is achieved. It is shown that a MATLAB realization of this algorithms can effectively recover high degree (≥ 2000)… (More)

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

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

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.

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

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.

An algorithm for fast and accurate evaluation of band-limited functions at many scattered points on the unit 2-d sphere is developed. The algorithm is based on trigonometric representation of spherical harmonics in spherical coordinates and highly localized tensor-product trigonometric kernels (needlets). It is simple, fast, local, memory efficient,… (More)

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

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

- Borislav R. Draganov, Kamen G. Ivanov
- Journal of Approximation Theory
- 2010

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 0 (1 + x) γ∞−γ 0 with arbitrary real γ0, 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 simple… (More)