We introduce a new variational method for the numerical homogenization of divergence
form elliptic, parabolic and hyperbolic equations with arbitrary rough (L∞) coefficients. Our …

In this article, a positive answer is given to the following question posed by Hayman [35,
page 326]: if a polyharmonic entire function of order k vanishes on k distinct ellipsoids in the …

Cardinal polysplines of order p on annuli are functions in C2p-2Rn⧹ 0 which are piecewise
polyharmonic of order p such that Δp-1S may have discontinuities on spheres in Rn …

In the classical theory of cubic interpolation splines there exists an algorithm which works
with only O n arithmetic operations. Also, the smoothing cubic splines may be computed via …

Explicit pointwise error bounds for the interpolation of a smooth function by piecewise
exponential splines of order four are given. Estimates known for cubic splines are extended …

In this paper a special class of one-dimensional L-splines of order 4 is studied, which
naturally appear in the computation of interpolation and smoothing with multivariate …

Polyharmonic functions f of infinite order and type τ on annular regions are systematically
studied. The first main result states that the Fourier-Laplace coefficients fk, l (r) of a …

In this paper it is shown that many features from polynomial spline methods used in
nonparametric regression and smoothing procedures carry over to the class of L-splines …

Let be a polyharmonic function of order N defined on the strip satisfying the growth condition
0.1 for and any compact subinterval K of, and suppose that vanishes on equidistant …

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