3 papers
math.CA2019
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…
math.CA2019
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: $$H_n(z; h)=\fracμ{n}\sum_{k=1}^n h(λ_k z),\quad \text{where}\quad μ,λ_…
math.CA2018
A family of singular integral operators which control the Cauchy transform
Petr Chunaev, Joan Mateu, Xavier Tolsa
We study the behaviour of singular integral operators of convolution type on associated with the parametric kernels $$ k_t(z):=\frac{(\Re z)^{3}}{|z|^{4}}+t\…