Hermite Interpolation of Data Sets by Minimal Spline SpacesSpringer Science and Business Media LLC - Tập 23 - Trang 211-227 - 2005
Manfred Sommer
Hermite interpolation of 2n + k data by spline spaces of order k with n variable knots counting multiplicities is studied. A characterization of the minimal spline spaces which admit a solution of the interpolation problem is obtained. A sufficient condition on uniqueness of interpolating spline functions is given.
The Vector-Valued Big q-Jacobi TransformSpringer Science and Business Media LLC - Tập 29 - Trang 85-127 - 2008
Wolter Groenevelt
Big q-Jacobi functions are eigenfunctions of a second-order q-difference operator L. We study L as an unbounded self-adjoint operator on an L
2-space of functions on ℝ with a discrete measure. We describe explicitly the spectral decomposition of L using an integral transform ℱ with two different big q-Jacobi functions as a kernel, and we construct the inverse of ℱ.
Vector-valued, rational interpolants IIISpringer Science and Business Media LLC - Tập 2 - Trang 263-289
C. D. Jenkins, P. R. Graves-Morris
In 1963, Wynn proposed a method for rational interpolation of vector-valued quantities given on a set of distinct interpolation points. He used continued fractions, and generalized inverses for the reciprocals of vector-valued quantities. In this paper, we present an axiomatic approach to vector-valued rational interpolation. Uniquely defined interpolants are constructed for vector-valued data so ...... hiện toàn bộ
#Numerical Analysis #Analysis
Almost Everywhere Convergence of Orthogonal Expansions of Several VariablesSpringer Science and Business Media LLC - Tập 22 - Trang 67-93 - 2004
Yuan Xu
For a weighted L1 space on the unit sphere of Rd+1, in which the
weight functions are invariant under finite reflection groups, a maximal
function is introduced and used to prove the almost everywhere convergence
of orthogonal expansions in h-harmonics. The result applies to various
methods of summability, including the de La Vallée Poussin means and the
Cesàro means. Similar results are also...... hiện toàn bộ
Asymptotics for Lp-norms of Fourier series density estimatorsSpringer Science and Business Media LLC - Tập 6 - Trang 375-397 - 1990
Lajos Horváth
LetX
1, X2, ⋯, be a sequence of independent, identically distributed bounded random variables with a smooth density functionf. We prove that
$$\int_a^b | f_{m,n} (t) - f(t)|^p w(t)dt(1 \leqslant p< \infty )$$
is asymptotically normal, wheref
m, n is the Fourier series density estimator offandw is a nonn...... hiện toàn bộ
PrefaceSpringer Science and Business Media LLC - Tập 9 Số 2-3 - Trang 121-121 - 1993
Ronald A. DeVore, Charles A. Micchelli