arXiv subjects

E. G. Kudasheva

Publications and source records attributed to E. G. Kudasheva.

4 recordsLinked to original sources

arXiv2023

Completeness of exponential systems in spaces of functions on a compact or domain and their area

We present new completeness conditions for exponential systems on the complex plane in Banach algebras of continuous functions on a compact with a connected complement that are simultaneously holomorphic in the interior of this compact if it is nonempty, as well as in spaces of holomorphic functions on a simply connected bounded domain with a topology of uniform convergence on compact subsets. These conditions are formulated in terms of the Euclidean area of the convex hull of a compact or a region on the one hand, and new characteristics of the distribution of exponential system indicators on the other.

math.CV↗

arXiv2023

Completeness of exponential systems and the perimeter of the convex hull

We give a new scale of completeness conditions for exponential systems in two types of functional spaces on subsets of the complex plane. The first is the Banach spaces of functions that are continuous on a compact and simultaneously holomorphic in the interior of this compact, if this interior is nonempty, with a uniform norm. The second is the spaces of holomorphic functions on a bounded open set with a topology of uniform convergence on compacts. These conditions are formulated in terms of the perimeter of the convex hull of the domain of determining of functions from space and new characteristics of distribution of exponents of exponential system.

math.CV↗

arXiv2023

Completeness of the exponential system in geometric terms of width, breadth and diameter

We establish a criterion for the completeness of an exponential system in the spaces of functions continuous on a convex compact set and holomorphic in the interior of this compact set, as well as in the spaces of holomorphic functions in the convex domain in terms of the breadth of the compact set or the domain in the direction. The main results are formulated exclusively through the relations between the breadth in the direction, width or diameter of the compact set or domain on the one hand and the logarithmic submeasures or logarithmic block densities of the distribution of exponents of exponential system on the other.

math.CV↗

arXiv2022

Subharmonic addition to the Beurling-Malliavin multiplier theorem

We prove a version of the Beurling-Malliavin multiplier theorem. This version is formulated here in a simplified form. Let $u\not\equiv -\infty$ and $M\not\equiv -\infty$ be a pair of subharmonic functions on the complex plane $\mathbb C$ with positive parts $u^+:=\sup\{u,0\}$ and $M^+$ such that $$ \operatorname{type}[u]:=\limsup_{z\to \infty} \frac{u^+(z)}{|z|}<+\infty, \qquad \operatorname{type}[M]<+\infty, \qquad \int_{-\infty}^{+\infty}\frac{u^+(x)+M^+(x)}{1+x^2}\operatorname{d}x<+\infty. $$ If $\operatorname{type}[u]<a<+\infty$, $0<b<+\infty$, and $\operatorname{type}[M]<c<+\infty$, then there are an entire function $h\not\equiv 0$ with $\operatorname{type}[\log|h|]<c$ and a subset $iY$ in the imaginary axis $i\mathbb R$ of linear Lebesgue measure $<b$ such that the function $h$ is bounded on the real axis and $u(z)-M(z)+\log|h(z)|\leq a|\Im z|$ on each straight line parallel to the real axis and not intersecting $iY$.

math.CV↗