Some remarks on interpolation and best approximation

Remarks on some interpolation spaces

One purpose of this paper is to introduce a new idea of associating microlocal measures to bounded functions of bounded variation, and even to functions in the interpolation space (H(Q)yL (Q))1.7oo, in order to replace and improve some methods from geometric measure theory. Some properties of similar interpolation spaces are reviewed first. I do not remember when I met Enrico MAGENES for the fi...

Some theorems and remarks on interpolation

Throughout this paper x"'), x-"1 ,. . ., x~,' will denote the roots of the n-th Chebyshev polynomial T " (x) [T " (cosh) = cos nJ]. f(x) will denote a function continuous in [-1, +1] and L,(f(x)) will denote the Lagrange interpolation polynomial of f(x) taken at the points xi(") (i = 1, 2,. . ., n) ; in other words, L,(f(x)) is a polynomial of degree not greater than (n-1) for which') L " (f(x+...

Some Remarks on Multilinear Maps and Interpolation

A multilinear version of the Boyd interpolation theorem is proved in the context of quasi-normed rearrangement-invariant spaces. A multilinear Marcinkiewicz interpolation theorem is obtained as a corollary. Several applications are given, including estimates for bilinear fractional integrals.

Some Remarks on Minimal Spline Interpolation

Interpolation of 2n+k data by spline spaces of order k with n knots is studied. Some conditions on existence of interpolating splines are given. Numerical methods for constructing a solution are suggested. Mathematics Subject Classification: 41A05, 41A15

Some Results on p-Best Approximation in Vector Spaces