Related papers: Real complex functions
A complex-analytic structure within the unit disk of the complex plane is presented. It can be used to represent and analyze a large class of real functions. It is shown that any integrable real function can be obtained by means of the…
In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and…
In the context of the correspondence between real functions on the unit circle and inner analytic functions within the open unit disk, that was presented in previous papers, we show that the constructions used to establish that…
We discuss various theorems about bounded analytic functions on the bidisk that were proved using operator theory.
We study boundary properties of plurisubharmonic functions near real submanifolds of almost complex manifolds.
In the context of the complex-analytic structure within the unit disk centered at the origin of the complex plane, that was presented in a previous paper, we show that a certain class of non-integrable real functions can be represented…
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…
For Banach spaces of analytic functions on the disc for which the polynomials are dense and their pointt evaluations continuous, we prove the following: If they contain a function such that the limit superior of its modulus is infinite…
We consider the connection of functional decompositions of rational functions over the real and complex numbers, and a question about curves on a Riemann sphere which are invariant under a rational function.
Under very general conditions it is shown that if $A$ is a uniform algebra generated by real-analytic functions, then either $A$ consists of all continuous functions or else there exists a disc on which every function in $A$ is holomorphic.…
In the context of the complex-analytic structure within the unit disk centered at the origin of the complex plane, that was presented in a previous paper, we show that the complete Fourier theory of integrable real functions is contained…
Real analytic generalized functions are investigated as well as the analytic singular support and analytic wave front of a generalized function in $\mathcal{G}(\Omega)$ are introduced and described.
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 consider a class $\THO$ of typically real harmonic functions on the unit disk that contains the class of normalized analytic and typically real functions. We also obtain some partial results about the region of univalence for this class.
In this paper we introduce certain analytic functions of boundary rotation bounded by $k\pi$ which are of Caratheodory origin. With them we study two classes of analytic and univalent functions in the unit disk $E=\{z\in \mathbb{C}\colon…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
Let $E$ be the open unit disk $\{z\in \mathbb{C}: |z|<1\}$. Let $A$ be the class of analytic functions in $E$, which have the form $f(z)=z+a_2z^2+...$. We define operators $L_n^\sigma\colon A\to A$ using the convolution *. Using these…
We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions,…
In these notes we consider power series representations of functions on the unit disk in the complex plane which define harmonic and holomorphic functions and related matters concerning boundary values, Poisson kernels, and so on.
Let U be the closed unit disc in C and let p be a point on the unit circle. Let f be a continuous function on U which extends holomorphically from each circle contained in U and centered at the origin, and from each circle contained in U…