307 citations · 338 across the 9 of their papers we have counts for
12 papers
Community detection in node-attributed social networks: a survey
Petr Chunaev
Community detection is a fundamental problem in social network analysis consisting in unsupervised dividing social actors (nodes in a social graph) with certain social connections…
Gorin's problem for individual simple partial fractions
Petr Chunaev, Vladimir Danchenko
The main result of the paper is a lower estimate for the moduli of imaginary parts of the poles of a simple partial fraction (i.e. the logarithmic derivative of an algebraic polyno…
Interpolation by generalized exponential sums with equal weights
Petr Chunaev
Here we solve Padé and Prony interpolation problems for the generalized exponential sums with equal weights: $$H_n(z; h)=\fracμ{n}\sum_{k=1}^n h(λ_k z),\quad \text{where}\quad μ,λ_…
A family of singular integral operators which control the Cauchy transform
Petr Chunaev, Joan Mateu, Xavier Tolsa
We study the behaviour of singular integral operators of convolution type on associated with the parametric kernels $$ k_t(z):=\frac{(\Re z)^{3}}{|z|^{4}}+t\…
Quadrature formulas with variable nodes and Jackson-Nikolskii inequalities for rational functions
Petr Chunaev, Vladimir Danchenko
We obtain new parametric quadrature formulas with variable nodes for integrals of complex rational functions over circles, segments of the real axis and the real axis itself. Basin…
Singular integrals unsuitable for the curvature method whose -boundedness still implies rectifiability
Petr Chunaev, Joan Mateu, Xavier Tolsa
The well-known curvature method initiated in works of Melnikov and Verdera is now commonly used to relate the -boundedness of certain singular integral operators to the geo…
A new family of singular integral operators whose -boundedness implies rectifiability
Petr Chunaev
Let be a Borel set such that . David and Léger proved that the Cauchy kernel (and even its coordinate parts $\textrm{Re}\, z…
Extremal and approximation properties of simple partial fractions
V. I. Danchenko, M. A. Komarov, P. V. Chunaev
In approximation theory, logarithmic derivatives of complex polynomials are called simple partial fractions (SPF) as suggested by Eu.P. Dolzhenko. Many solved and unsolved extremal…
Approximation by amplitude and frequency operators
Petr Chunaev, Vladimir Danchenko
We study Padé interpolation at the node of functions , analytic in a neighbourhood of this node, by amplitude and frequency operators (sums)…
On Hölder and Minkowski Type Inequalities
Petr Chunaev, Ljiljanka Kvesić, Josip Pečarić
We obtain inequalities of Hölder and Minkowski type with weights generalizing both the case of weights with alternating signs and the classical case of non-negative weights.
Logarithmic Derivatives of Least Deviation from Zero
Petr Chunaev
We study least deviation of logarithmic derivatives of real-valued polynomials with a fixed root from zero on the segment in the uniform norm with the weight $\sqrt{1-x^2}…
Hölder and Minkowski Type Inequalities with Alternating Signs
Petr Chunaev
We obtain new inequalities with alternating signs of Hölder and Minkowski type.