Browsing by Subject "integral operators"

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Access status: Open Access ,
Eigenvalue asymptotics for potential type operators on Lipschitz surfaces of codimension greater than 1
(Wydawnictwa AGH, 2018) Rozenblûm, Grigorij Vadimovič; Taŝiân, Grigorij Mihajlovič
For potential type integral operators on a Lipschitz submanifold the asymptotic formula for eigenvalues is proved. The reasoning is based upon the study of the rate of operator convergence as smooth surfaces approximate the Lipschitz one.
Access status: Open Access ,
On some classes of meromorphic functions defined by subordination and superordination
(2011) Totoi, Alina
Let $p\in \mathbb{N}^*$ and $\beta,\gamma\in \mathbb{C}$ with $\beta\neq 0$ and let $\Sigma_p$ denote the class of meromorphic functions of the form $g(z)=\frac{a_{-p}}{z^p}+a_0+a_1 z+\ldots,\,z\in \dot U$, $a_{-p}\neq 0$. We consider the integral operator $J_{p,\beta,\gamma}:K_{p,\beta,\gamma}\subset\Sigma_p\to \Sigma_p$ defined by $J_{p,\beta,\gamma}(g)(z)=\left[\frac{\gamma-p\beta}{z^\gamma }\int_0^zg^{\beta}(t) t^{\gamma-1}dt\right]^{\frac{1}{\beta}},\,g\in K_{p,\beta,\gamma},\,z\in \dot U.$ We introduce some new subclasses of the class $\Sigma_p$, associated with subordination and superordination, such that, in some particular cases, these new subclasses are the well-known classes of meromorphic starlike functions and we study the properties of these subclasses with respect to the operator $J_{p,\beta,\gamma}$.