Related papers: An extremal problem for a class of entire function…

We obtain sufficient conditions for an exponential type entire function not to have zeros in the open lower half-plane. An exact inequality containing the real and imaginary parts of such functions and their derivatives restricted to the…

Let $\mu$ be a finite positive measure on the real line. For $a>0$ denote by $\EE_a$ the family of exponential functions $$\EE_a=\{e^{ist}| \ s\in[0,a]\}.$$ The exponential type of $\mu$ is the infimum of all numbers $a$ such that the…

We consider the problem of determining the inducibility (maximum possible asymptotic density of induced copies) of oriented graphs on four vertices. We provide exact values for more than half of the graphs, and very close lower and upper…

We discuss the problem where the extremal function in embedding theorem of some (generally speaking, non-integer) order is the constant function. We obtain the necessary and sufficient conditions of this.

The paper is devoted to the study of the unconditional extremal problem for a fractional linear integral functional defined on a set of probability distributions. In contrast to results proved earlier, the integrands of the integral…

We study the uniqueness of optimal solutions to extremal graph theory problems. Lovasz conjectured that every finite feasible set of subgraph density constraints can be extended further by a finite set of density constraints so that the…

For a real constant $b,$ we give sharp estimates of $\log|f(z)/z|+b\arg[f(z)/z]$ for subclasses of normalized univalent functions $f$ on the unit disk.

We solve two continuous extremal problems on the classes of monotone functions: in the first problem we find extremal values for a line integral of a coordinate-wise monotone function of two variables from a rearrange\-ment-invariant class…

We study the exponential decay of relative entropy functionals for zero-range processes on the complete graph. For the standard model with rates increasing at infinity we prove entropy dissipation estimates, uniformly over the number of…

Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied…

Determination of linear combination of exponential functions with unknown rate constants from its sampled values is a problem of considerable interest. Here we present a constructive and explicit solution to this problem. Moments of such…

We give a complete description of zero sets for some well-known subclasses of entire functions of exponential growth (bounded on real axis, Cartwright's class)

For a family $\mathcal{F}$ of graphs, let $ex(n,\mathcal{F})$ denote the maximum number of edges in an $n$-vertex graph which contains none of the members of $\mathcal{F}$ as a subgraph. A longstanding problem in extremal graph theory asks…

We generalized the Korkin-Zolotarev theorem to the case of entire functions having the smallest $L^1$ norm on a system of intervals $E$. If $\bbC\setminus E$ is a domain of Widom type with the Direct Cauchy Theorem we give an explicit…

Let $E= A - iB$ be a Hermite-Biehler entire function of exponential type $\tau/2$ where $A$ and $B$ are real entire, and consider $d\mu(x) = dx/|E(x)|^2$. We show that the sign of the product $A B$ is an extremal signature for the space of…

We solve an extremal problem that arises in the study of the refractive indices of passive metamaterials. The problem concerns Hermitian functions in $H^2$ of the upper half-plane, i.e., $H^2$ functions satisfying $f(-x)=\bar{f(x)}$. An…

We generalize the concept of extremal index of a stationary random sequence to the series scheme of identically distributed random variables with random series sizes tending to infinity in probability. We introduce new extremal indices…

We study a specific convex maximization problem in the space of continuous functions defined on a semi-infinite interval. An unexplained connection to the discrete version of this problem is investigated.

We look for pointwise bounds on a plurisubharmonic function near its singularity point, given the value of its generalized Lelong number with respect to a plurisubharmonic weight. To this end, an extremal problem is considered. In certain…

We obtain sharp estimates for the quasi norm of the maximal function of f when it satisfies certain conditions.