Approximation Of Periodic Functions Research Articles

A method of designing cam mechanisms by means of piecewise-circular curves

An algorithm is obtained that permits one to describe cam mechanisms with flat pushers by smooth piecewise curves constructed from arcs of circles. The algorithm is based on the approximation of periodic functions by Hermitian local trigonometrical splines.

On the order of local approximation of functions by trigonometric polynomials that are partial sums of averaging operators

We study the order of polynomial approximations of periodic functions on intervals which are internal with respect to the main interval of periodicity and on which these functions are sufficiently smooth. The estimates obtained contain parameters which characterize the smoothness and alternation of signs of nuclear functions and parameters that determine classes of approximated functions.

Norm approximation of periodic functions from noisy Fourier coefficients

Norm approximation of periodic functions from noisy Fourier coefficients

Inverse theorems on approximation of periodic functions

We obtain new inverse theorems on the approximation of periodic functions f(·) that establish conditions for the existence of their (ψ, β)-derivatives. These theorems also guarantee a certain smoothness of these derivatives.

Approximation of periodic functions by constants in the metric spaces ?p(L)

By using the best approximations of functions by constants, we establish necessary conditions for the moduli of continuity of periodic functions in metric spaces with integral metric and find the Young constants of these spaces.

Approximation of periodic functions by Fejer-Zygmund means in various metrics

Approximation of periodic functions by Fejer-Zygmund means in various metrics

Approximation of periodic functions by interpolation polynomials in L1

Asymptotically precise estimates are obtained for the deviation, in the L1-norm, of interpolation polynomials with equally-spaced nodes from certain classes of functions.

Approximation of functions of several variables by trigonometric polynomials with harmonics from hyperbolic crosses

their Fourier series," Mat. Zametki, ~, 291-300 (1968). 13. S. B. Stechkin, "An estimation of the remainders of the Fourier series of differentiable functions," Tr. Mat. Inst. Akad. Nauk SSSR, 145, 126-151 (1980). 14. A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987). 15. H. B. Dwight, Tables of Integrables and Other Mathematical Data, 4th edn., The Macmillan Company, New York (1961). 16. S. M. Nikol'skii, "Approximation of functions in the mean by trigonometric polynomials," Izv. Akad. Nauk SSSR, Ser. Mat., i0, 207-256 (1946). 17. N. I. Akhiezer, Lectures on Approximation Theory [in Russian], Nauka, Moscow (1965). 18. S. B. Stechkin and S. A. Telyakovskii, "On approximation of differentiable functions by trigonometric polynomials in the L metric," Tr. Mat. Inst. Akad. Nauk SSSR, 88, 20-29 (1967).

Dzydyk's research on the theory of approximation of periodic functions

Dzydyk's research on the theory of approximation of periodic functions

Jackson's inequality for mean-square approximations of periodic functions by trigonometric polynomials on a uniform grid

Jackson's inequality for mean-square approximations of periodic functions by trigonometric polynomials on a uniform grid

Some sharp inequalities for approximations of periodic functions in $L_1$ space

We provide sharp estimates of Jackson's inequalities type for the best $(\alpha, \beta)$-approximations in the space $L_1$ of periodic functions that are representable as the convolution of the kernel $K$ that does not increase the number of sign alternations with functions $\varphi \in C$, by means of convolutions of the kernel $K$ with the functions that are piecewise-constant in the intervals $\bigl( \frac{l \pi}{n}, \frac{(l+1)\pi}{n} \bigr)$.

Approximation of periodic functions in LP by linear positive methods and multiple moduli of continuity

If the operator A is positive, i.e., K(t) _> 0, then it is known that in the case of p = i, estimate (3) is good enough, in the sense that its application leads to the precise value of the deviation on various classes of functions. However, for the values p ~ i, = estimate (3) is already rough, which is related to the strict convexity of the corresponding spaces Lp. Our goal is to obtain a more precise than (3) estimate of approximation by positive operators, which would reduce to the equality for a sufficiently wide class of functions. In doing so, we shall use the following variant of the Riesz-Thorin theorem on complex interpolation of operators in the spaces Lp with mixed norm, contained in [i]. Let LDr (i < p, r < ~) be the space of 2~-periodic in each argument complex functiorls g(x, t) such that

Jackson theorems in Hardy spaces and approximation by Riesz means

An analog of the theorem of D. Jackson on the approximation of periodic functions by means of trigonometric polynomials is established for some Hardy spaces of several variables.

On Strong Summability of Multiple Fourier Series and Approximation of Periodic Functions

On Strong Summability of Multiple Fourier Series and Approximation of Periodic Functions

Approximation of periodic functions by Zygmund means

Approximation of periodic functions by Zygmund means

Approximation of periodic functions by Fourier sums in the mean

Approximation of periodic functions by Fourier sums in the mean

Strong local theorems for approximation of periodic functions of many variables

Strong local theorems for approximation of periodic functions of many variables

Approximation of Periodic Functions by the Euler and Borel Means of Fourier Series

Approximation of Periodic Functions by the Euler and Borel Means of Fourier Series

Joint approximation of periodic functions and their derivatives by the Fourier and the Vallee Poussin sums in the metric of L

Joint approximation of periodic functions and their derivatives by the Fourier and the Vallee Poussin sums in the metric of L

Simultaneous approximation of periodic functions and their derivatives

Simultaneous approximation of periodic functions and their derivatives