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Monosplines of minimal norm and the best quadrature formulae
CONTENTS Introduction § 1. On spline functions § 2. Closures of sets of monosplines § 3. Theorems on zeros of monosplines § 4. Extremal properties of a monospline with multiple nodes § 5. ExistenceExpand
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The fundamental theorem of algebra for monosplines with multiple nodes
On etablit les conditions necessaires et suffisantes d'existence des fonctions monosplines a nœuds multiples ayant des zeros en des points donnes avec des multiplicites donnees
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SPLINE APPROXIMATION AND OPTIMAL RECOVERY OF OPERATORS
The problem of optimal recovery, on the basis of exact or erroneous information, of symmetry-preserving operators on sets of elements of convolution type is solved. Using the information operator andExpand
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On monosplines with nonnegative coefficients
On etablit quelques inegalites pour les fonctions monosplines et on les applique aux meilleures formules de quadrature pour certaines classes de fonctions a norme non symetrique
One property of best quadrature formulas
AbstractIt is established that for classWpr (r=i, 2, ...; 1⩽p⩽∞) the best quadrature formulas of the form $$\int_0^1 {f\left( x \right)dx = } \Sigma _{k = 0}^\rho \mathop {\Sigma _{i = 1}^nExpand
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Recovery problems on sets of multivariate functions by accurate data
AbstractПолучены точные по порядку относителяно количества единиц информации методы восстановления операторов на классах функции, представимых в виде суммы Элементов типа свертки с ограничениями вExpand
Nonlinear interpolation and norm minimization
We prove that the set of convolution-type functions in ℝd that satisfy the interpolation conditions contains a unique function whose convolution element has the minimumLp-norm. The extremal functionExpand
Exact bounds for the uniform approximation of continuous periodic functions by r-th order splines
We solve the problem of determining exact bounds for the uniform approximation of continuous periodic functions by r-th order interpolation splines in a space C and on a class Hω specified by theExpand
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