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The main goal of this article is to bring together the theories of holomorphic iteration in the unit disc and semigroups of holomorphic functions. We develop a technique that allows us to partially embed the orbit of a holomorphic self-map…
The purpose of this paper is to present a solution to perhaps the final remaining case in the line of study concerning the generalization of Forelli's theorem on the complex analyticity of the functions that are: (1) $\mathcal{C}^\infty$…
We obtain recurrences for smallest parts functions which resemble Euler's recurrence for the ordinary partition function. The proofs involve the holomorphic projection of non-holomorphic modular forms of weight 2.
In this paper, pointwise convergence, uniform convergence and compact convergence of sequences of holomorphic functions on an open subset of the complex plane are compared from a linear point of view. In fact, it is proved the existence of…
Our objective in this paper is to introduce and investigate comprehensive-constructed subclasses of normalized analytic and bi-univalent functions on the unit open disc. Bounds for the second and third Tayler-Maclaurin coefficients of…
The decompositions of an element of a finite von Neumann algebra into the sum of a normal operator plus an s.o.t.-quasinilpotent operator, obtained using the Haagerup--Schultz hyperinvariant projections, behave well with respect to…
In this paper, we continue to develop the theory of free holomorphic functions on noncommutative regular polydomains. We find analogues of several classical results from complex analysis such as Abel theorem, Hadamard formula, Cauchy…
Some Dirichlet-like functions, attached to a pair (periodic function, polynomial) are introduced and studied. These functions generalize the standard Dirichlet L-functions of Dirichlet characters. They have similar properties, being…
We construct a H\"older continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We say that a function with…
Given a topological group $ G $ and a Hausdorff topological group $ A $ on which $ G $ acts continuously and compatibly with the group operation of $ A $, we study the set of continuous cocycles of $ G $ with value in $ A $. This set is a…
We introduce the concept of F-decomposable systems, well-ordered inverse systems of Hausdorff compacta with fully closed bonding mappings. A continuous mapping between Hausdorff compacta is called fully closed if the intersection of the…
The classical Hurwitz theorem says that if n first "harmonics" (2n + 1 Fourier coefficients) of a continuous function f(x) on the unit circle are zero, then f(x) changes sign at least 2n + 1 times. We show that similar facts and its…
The Dehn function measures the area of minimal discs that fill closed curves in a space; it is an important invariant in analysis, geometry, and geometric group theory. There are several equivalent ways to define the Dehn function, varying…
A method of constructing an entire function with given zeros and estimates of growth is suggested. It gives a possibility to describe zero sets of certain classes of entire functions of one and several variables in terms of growth of volume…
In this short article we show an orthogonal decomposition of a Hilbert space as a sum of null solutions of the first derivative and the first derivative of a traceless higher order Hilbert/Sobolev space. We define orthogonal projections and…
For functions in the Sobolev space $H^s$ and decreasing sequences $t_n\to 0$ we examine convergence almost everywhere of the generalized Schr\"odinger means on the real line, given by \[S^af(x,t_n)=\exp( it_n (-\partial_{xx})^{a/2})f(x);\]…
We study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are…
While discrete harmonic functions have been objects of interest for quite some time, this is not the case for discrete polyharmonic functions, as appear for instance in the asymptotics of path counting problems. In this article, a novel…
We introduce $p$-adic Kummer spaces of continuous functions on $\mathbb{Z}_p$ that satisfy certain Kummer type congruences. We will classify these spaces and show their properties, for instance, ring properties and certain decompositions.…
The fractional polylogarithms, depending on a complex parameter $\a$, are defined by a series which is analytic inside the unit disk. After an elementary conversion of the series into an integral presentation, we show that the fractional…