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2000 Mathematics Subject Classification: 41A25, 41A36.The purpose of this paper is to present a characterization of a certain Peetre K-functional in Lp[−1,1] norm, for 1 ≤ p ≤ 2 by means of a modulus of smoothness. This modulus is based on the classical one taken on a certain linear transform of the function.

A class of Cardinal Lacunary interpolation problems by spline functions.

S.L. Lee (1978)

Aequationes mathematicae

A class of generalized best approximation problems in locally convex linear topological spaces.

Samanta, Hora Krishna (1997)

International Journal of Mathematics and Mathematical Sciences

A class of generalized uniform asymptotic expansions.

Obi, Wilson C. (1978)

International Journal of Mathematics and Mathematical Sciences

A Class of Multidimensional Periodic Splines.

Willi Freeden, Richard Reuter (1981)

Manuscripta mathematica

A classification of projectors

Gustavo Corach, Alejandra Maestripieri, Demetrio Stojanoff (2005)

Banach Center Publications

A positive operator A and a closed subspace of a Hilbert space ℋ are called compatible if there exists a projector Q onto such that AQ = Q*A. Compatibility is shown to depend on the existence of certain decompositions of ℋ and the ranges of A and $A^{1 / 2}$ . It also depends on a certain angle between A() and the orthogonal of .

A commutant lifting theorem on analytic polyhedra

Calin Ambrozie, Jörg Eschmeier (2005)

Banach Center Publications

In this note a commutant lifting theorem for vector-valued functional Hilbert spaces over generalized analytic polyhedra in ℂⁿ is proved. Let T be the compression of the multiplication tuple $M_{z}$ to a *-invariant closed subspace of the underlying functional Hilbert space. Our main result characterizes those operators in the commutant of T which possess a lifting to a multiplier with Schur class symbol. As an application we obtain interpolation results of Nevanlinna-Pick and Carathéodory-Fejér type...

A compact set without Markov’s property but with an extension operator for $C^{\infty}$ -functions

Alexander Goncharov (1996)

Studia Mathematica

We give an example of a compact set K ⊂ [0, 1] such that the space ℇ(K) of Whitney functions is isomorphic to the space s of rapidly decreasing sequences, and hence there exists a linear continuous extension operator $L : ℇ (K) \to C^{\infty} [0, 1]$ . At the same time, Markov’s inequality is not satisfied for certain polynomials on K.

A comparative analysis of Bernstein type estimates for the derivative of multivariate polynomials

Szilárd Gy. Révész (2006)

Annales Polonici Mathematici

We compare the yields of two methods to obtain Bernstein type pointwise estimates for the derivative of a multivariate polynomial in a domain where the polynomial is assumed to have sup norm at most 1. One method, due to Sarantopoulos, relies on inscribing ellipses in a convex domain K. The other, pluripotential-theoretic approach, mainly due to Baran, works for even more general sets, and uses the pluricomplex Green function (the Zaharjuta-Siciak extremal function). When the inscribed ellipse method...

A comparison of three high-precision quadrature schemes.

Bailey, David H., Jeyabalan, Karthik, Li, Xiaoye S. (2005)

Experimental Mathematics

A Computational Procedure for the Approximation of Random Functions.

W.H. Ling, H.W. McLaughlin, M.L. Smith (1976/1977)

Numerische Mathematik

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