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 …

Let L be a linear differential operator with constant coefficients of order n and complex
eigenvalues λ 0,…, λ n. Assume that the set U n of all solutions of the equation Lf= 0 is …

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 …

Despite their frequent use in our daily life, the expansion and reduction of images are
among the least studied research areas in the literature. That is why the present research …

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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