I. Sheipak

activity

20072022

most citedDegenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes

8 citations · 10 across the 8 of their papers we have counts for

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math.FA2022

Exact estimates of high-order derivatives in Sobolev spaces

T. A. Garmanova, I. A. Sheipak

The paper describes the splines $Q_{n, k} (x, a)$ , which for an arbitrary point $a \in (0; 1)$ and an arbitrary function $y \in W ˚_{p}^{n} [0; 1]$ set the relations $y^{(k)}(a)=\int_0^…

math.FA2020

Explicit Form Of Extremal Functions In The Embedding Constant Problem For Sobolev SpacesI

Igor Sheipak, Tatiana Garmanova

The embedding constants of the Sobolev spaces $W ˚_{2}^{n} [0; 1] ↪ W ˚_{\infty}^{k} [0; 1]$ ( $0 ⩽ k ⩽ n - 1$ ) are studied. A relation of the embe…

math.FA2018

On Hölder exponents of the self-similar functions

Igor Sheipak

We study the class of affine self-similar and continuous on interval $[0; 1]$ functions. Formulas for the Hölder exponents are obtained in terms of self-similarity parameters.

math.FA2009

On spectrum of Jacobi operator with exponentially increasing matrix elements

I. A. Sheipak

The class of three-diagonal Jacobi matrix with exponentially increasing elements is considered. Under some assumptions the matrix corresponds to unbounded self-adjoint operator in…

math.FA2007

The singular points of self-similar functions with zero spectral degree. Stieltjes self-similar string

I. A. Sheipak

The self-similar functions of zero spectral degree are defined. The singular points of these functions are investigated and full classification of points is given. The connection w…