arXiv subjects

Valentin V. Andreev

Publications and source records attributed to Valentin V. Andreev.

4 recordsLinked to original sources

arXiv2026

Remark Concerning Cesáro Operator on the Hardy Space $H^p(\mathbb{C}_+)$ in the Upper Half-Plane

We consider Cesáro operator on the Hardy space $H^p(\mathbb{C}_+)$ in the upper half-plane for $1<p<\infty$. In \cite{AS} it was proved that for all $1<p<\infty$ the spectrum of the operator $V=\frac{2(p-1)}{p}C-I$ is located on the unit circle and in \cite{ABC1} the authors of this note showed that for $p=2$ operator $V$ is unitary. In the present note we show that for $1<p<\infty$, $p\ne 2$, the norm of the operator $V$ is strictly greater than one.

math.FA↗

arXiv2024

On Generators of the Hardy and the Bergman Spaces

A function which is analytic and bounded in the Unit disk is called a generator for the Hardy space or the Bergman space if polynomials in that function are dense in the corresponding space. We characterize generators in terms of sub-spaces which are invariant under multiplication by the generator and also invariant under multiplication by z, and study wandering properties of such sub-spaces. Density of bounded analytic functions in the sub-spaces of the Hardy space which are invariant under multiplication by the generator is also investigated.

math.CV↗

arXiv2024

On the Ces`aro operator on the Hardy space in the upper half-plane

We discuss the Ces`aro operator on the Hardy space in the upper half-plane. We provide a new simple proof of the boundedness of this operator, prove that this operator is equal to the sum of the identity operator and a unitary operator, which implies its normality.

math.FA↗

arXiv2013

Computing conformal maps onto circular domains

We show that, given a non-degenerate, finitely connected domain $D$, its boundary, and the number of its boundary components, it is possible to compute a conformal mapping of $D$ onto a circular domain \emph{without} prior knowledge of the circular domain. We do so by computing a suitable bound on the error in the Koebe construction (but, again, without knowing the circular domain in advance). As a scientifically sound model of computation with continuous data, we use Type-Two Effectivity.

math.CV↗