Related papers: On Limits of Sequences of Holomorphic Functions

We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on…

We give a new characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The characterization is new even in Euclidean spaces and it holds also in…

The theory of holomorphic functions of several complex variables is applied in proving a multidimensional variant of a theorem involving an exponential boundedness criterion for the classical moment problem. A theorem of Petersen concerning…

We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula, and study their limit in the continuum.

Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…

We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.

This paper is devoted to investigating the sequence of some linear functionals in the space $BV$ of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In…

We consider various notions of holomorphic extendability of complex valued functions defined on subsets of $\mathbf C^n$, including one-sided extendability. We show that in the relevant function spaces, these phenomena of holomorphic…

Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.

The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…

We study the behavior of various set-functions under holomorphic motions. We show that, under such deformations, logarithmic capacity varies continuously, while analytic capacity may not.

We discuss meromorphic functions on the complex plane which are Brody curves regarded as holomorphic maps to P_1, i.e., which have bounded spherical derivative.

We set new dual problems for the weighted spaces of holomorphic functions of one variable in domains on the complex plane, namely: nontriviallity of a given space, description of zero sets, description of (non-)uniqueness sets, the…

Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…

Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.

We present a comprehensive survey on removability of compact plane sets with respect to various classes of holomorphic functions. We also discuss some applications and several open questions, some of which are new.

A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the…

We provide a description of the interpolating and sampling sequences on a space of holomorphic functions with a uniform growth restriction defined on finite Riemann surfaces.

We study noncommutative versions of holomorphic and harmonic functions on the unit disk.

We develop a new technique for studying the boundary limiting behavior of a holomorphic function on a domain $\Omega$ -- both in one and several complex variables. The approach involves two new localized maximal functions. As a result of…