8 citations · 10 across the 8 of their papers we have counts for
9 papers
Exact estimates of high-order derivatives in Sobolev spaces
T. A. Garmanova, I. A. Sheipak
The paper describes the splines , which for an arbitrary point and an arbitrary function set the relations $y^{(k)}(a)=\int_0^…
Explicit Form Of Extremal Functions In The Embedding Constant Problem For Sobolev SpacesI
Igor Sheipak, Tatiana Garmanova
The embedding constants of the Sobolev spaces () are studied. A relation of the embe…
On Hölder exponents of the self-similar functions
Igor Sheipak
We study the class of affine self-similar and continuous on interval functions. Formulas for the Hölder exponents are obtained in terms of self-similarity parameters.
On the Neumann problem for Sturm-Liouville equation with self-similar Cantor type weight
A. A. Vladimirov, I. A. Sheipak
Sturm-Liouville problem with generalized derivative of self-similar Cantor type function as a weight is considered. Under Neumann and mixed boundary conditions the oscillating prop…
Asymptotics of eigenvalues of high-order differential operator with discrete self-similar weight
A. A. Vladimirov, I. A. Sheipak
The spectral problem for the high order differential operator with singular weight is considered. If the weight is a generalized derivative of self-similar function with zero spect…
Degenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes
A. I. Nazarov, I. A. Sheipak
We find the logarithmic small ball asymptotics for the -norm with respect to a degenerate self-similar measures of a certain class of Gaussian processes including Brownian mot…