Approximation Of Unbounded Functions Research Articles

Approximation of Unbounded Functions by Trigonometric Polynomials

Approximation of Unbounded Functions by Trigonometric Polynomials

Approximation of Unbounded Functions by Linear Positive Operators

A unified class of linear positive operators has been defined. Using these operators some approximation estimates have been obtained for unbounded functions. For particular linear positive operators these results sharpen and improve the earlier estimates due to Fuhua Cheng (J. Approx. Theory, 1984) and Xiehua Sun (J. Approx. Theory, 1988).

On approximation of unbounded functions by linear combinations of modified Szász-Mirakian operators

On approximation of unbounded functions by linear combinations of modified Szász-Mirakian operators

Hankel operators and problems of best approximation of unbounded functions

For each function f, f ε VMO, there exists a unique function f0, analytic in the circle $$\mathbb{D}$$ and such that ∥f−f0∥∞=f{∥∞∶gεVMOA}. We define the operator of best approximation (nonlinear) A, Af=f0, fεVMO, In the paper one considers the question of the preservation of a class under the action of the operator i.e. finding the classes X, X ⊂ VMO, AX ⊂ X. One investigates the classes X containing unbounded functions. It is proved that if P_X is the space of the symbols of the Hankel operators from a Banach space E of functions into the Hardy space H2, then AX ⊂ X. For E one can take “almost” any space.

Unbounded functions and positive linear operators

The approximation of unbounded functions by positive linear operators under multiplier enlargement is investigated. It is shown that a very wide class of positive linear operators can be used to approximate functions with arbitrary growth on the real line. Estimates are given in terms of the usual quantities which appear in the Shisha-Mond theorem. Examples are provided.

Approximation of unbounded functions and applications to representations of semigroups

The purpose of this paper is to study the approximation of functions in m variables and its application to semigroup representation. First, two Bohman-Korovkin-type theorems are established for the respective approximations of unbounded, operator-valued and real-valued functions with noncompact supports in R m. Then we investigate several approximation operators; some of them are generalizations (to m dimensions) of well-known linear positive operators and some are apparently new. Finally, through these operators, the first approximation theorem provides a unified approach to a whole set of representation formulas for m-parameter ( C 0)-semigroups of operators; special cases include well-known formulas due to Hille, Phillips, Widder, Kendall and Chung, as well as some new ones.

Approximation of unbounded functions on unbounded interval

Approximation of unbounded functions on unbounded interval

On the Order of Approximation of Unbounded Functions by Positive Linear Operators

Recently there has been a great amount of research both qualitative and quantitative on the problem of approximating functions with certain growth conditions by means of linear positive operators. This paper discusses a quantitative problem for unbounded functions, i.e., the order of approximation to unbounded functions by means of linear positive operators.The theorems presented are, in several instances, extensions of known results from the case of bounded functions to the unbounded case. Applications of these theorems are given to spline functions, which are presently the subject of intensive investigation, and to the well-known Szasz-Mirakyan-Hille operators.