A best approximation property of the generalized spline functions.
A Best Lower Bound for Good Lattice Points.
A certain class of quadratures.
A certain class of quadratures with hat function as a weight function.
A Characterization of C(X) Among Algebras on Planar Sets by the Existence of a Finite Universal Korovkin System.
A Characterization of Multivariate Quasi-interpolation Formulas and its Applications.
A characterization of random approximations.
A characterization of strictly convex metric linear spaces.
A characterization of the approximation order for multivariate spline spaces
A Characterization Theorem for the K-functional Associated with the Algebraic Version of Trigonometric Jackson Integrals
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.
A class of generalized best approximation problems in locally convex linear topological spaces.
A class of generalized uniform asymptotic expansions.
A Class of Multidimensional Periodic Splines.
A classification of projectors
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 . It also depends on a certain angle between A() and the orthogonal of .
A commutant lifting theorem on analytic polyhedra
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 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 -functions
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 . 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
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.
A Computational Procedure for the Approximation of Random Functions.