Related papers: Notes on functions on the unit disk
We study noncommutative versions of holomorphic and harmonic functions on the unit disk.
In trigonometric series terms all polyharmonic functions inside the unit disk are described. For such functions it is proved the existence of their boundary values on the unit circle in the space of hyperfunctions. The necessary and…
We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications…
These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, using quaternions and Clifford algebras in higher dimensions. The main themes are weak solutions, the mean-value property, and subharmonicity.
We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion…
We introduce and develop the notion of spherical polyharmonics, which are a natural generalisation of spherical harmonics. In particular we study the theory of zonal polyharmonics, which allows us, analogously to zonal harmonics, to…
We survey a few classes of analytic functions on the disk that have real boundary values almost everywhere on the unit circle. We explore some of their properties, various decompositions, and some connections these functions make to…
This paper develops theory for a newly-defined bicomplex hyperbolic harmonic function with four real-dimensional inputs, in a way that generalizes the connection between real harmonic functions with two real-dimensional inputs and complex…
In this paper we study the boundary values of harmonic and holo- morphic functions in the weighted Hardy spaces on the unit disk $\mathbb{D}$. These spaces were introduced by Poletsky and Stessin in [6] for plurisubharmonic functions on…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on…
In this paper, we give several characterizations of Herglotz-Nevanlinna functions in terms of a specific type of positive semi-definite functions called Poisson-type functions. This allows us to propose a multidimensional analogue of the…
In this note we consider some generalizations of the Schwarz lemma for harmonic functions on the unit disk, whereby values of such functions and the norms of their differentials at the point $z=0$ are given.
n this article we consider functions meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. We include few open problems for…
We consider two parametric families of special functions: One is defined by a power series generalizing the classical Mathieu series, and the other one is a generalized Mathieu type power series involving factorials in its coefficients.…
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
We construct a set of quaternionic metamonogenic functions (that is, in $\mbox{Ker}(D+\lambda)$ for diverse $\lambda$) in the unit disk, such that every metamonogenic function is approximable in the quaternionic Hilbert module $L^2$ of the…
This note provides a complete description of a family of sense preserving harmonic functions in the open unit disk that have the same Jacobians, provided that one of the representatives of this family is known.
A subclass of complex-valued close-to-convex harmonic functions that are univalent and sense-preserving in the open unit disc is investigated. The coefficient estimates, growth results, area theorem, boundary behavior, convolution and…
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…