Estimate For Modulus Of Continuity Research Articles

On the Classification of Functions Integrable on a Segment

We study the problem of classification of functions integrable on a segment. Estimates for the integral moduli of continuity are obtained for functions from generalized Potapov’s classes.

On Constants in the Generalized Jackson Theorem

We consider the generalized Jackson theorem concerning estimates for the best approximation by trigonometric polynomials via the moduli of continuity of an arbitrary order. We improve the known estimates for moduli of continuity of the 4th and 6th order. Bibliography: 8 titles.

On the integral modulus of continuity of Fourier series

We study Lp-integrability (1<p<∞) of a sum φ of trigonometric series under the assumptions that the sequence of coefficients of φ belongs to the class \(\overline{\mathrm{GM}}_{\theta}^{r}\). Then we discuss the relations between the properties of φ and the properties of the sequence (λn)∈GM(β,r), and deduce an estimate for modulus of continuity of φ in Lp norm.

On Moduli of Continuity for Local Times of Fractional Stable Processes

We establish estimates for moduli of continuity of the local times of a class of self-similar stable processes. Our arguments yield also sharp lower bounds for the Hausdorff measure of the level sets of these processes. Finally, we prove the continuity in law of the local times with respect to the self-similarity index for a wide class of self-similar stable processes.

On the integral modulus of continuity of Fourier series

We obtain an estimate for the integral modulus of continuity of orderk of Fourier series with coefficients satisfying:a v →0 and Σ v=1 ∞ v 2|Δ2(a v /v)|<∞.

On the integral modulus of continuity of fourier series

We obtain an estimate for the integral modulus of continuity of orderk of Fourier series with coefficients satisfying:a v →0 and Σ v=1 ∞ v 2|Δ2(a v /v)|<∞.