相关论文: Almost periodicity in complex analysis

We give a characterization for two different concepts of quasi-analyticity in Carleman ultraholomorphic classes of functions of several variables in polysectors. Also, working with strongly regular sequences, we establish generalizations of…

In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous…

We consider summability methods generated by the class GM(2b). We generalize some related results of P. Pych-Taberska [Studia Math. XCVI (1990), 91-103] on strong approximation of almost periodic functions by their Fourier series and S. M.…

In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties…

We give a brief review of holomorphic motions and its relation with quasiconformal mapping theory. Furthermore, we apply the holomorphic motions to give new proofs of famous Konig's Theorem and Bottcher's Theorem in classical complex…

This is a survey about certain "almost homomorphisms" and "almost linear" functionals (called quasi-morphisms and quasi-states) in symplectic topology and their applications to Hamiltonian dynamics, functional-theoretic properties of…

The almost periodic functions form a natural example of a non-separable normed space. As such, it has been a challenge for constructive mathematicians to find a natural treatment of them. Here we present a simple proof of Bohr's fundamental…

For metrizable spaces we replace the notion of almost periodic homeomorphism with a similar notion and verify that the usual characterizations of almost periodic homeomorphisms of compact metric spaces are valid for all metrizable spaces.

An almost periodic function in finite-dimensional space extends to a holomorphic bounded function in a tube domain with a cone in the base if and only if the spectrum belongs to the conjugate cone. Also, an almost periodic function in…

In the present paper, we discuss several basic properties of a class of quasiconformal close-to-convex harmonic mappings with starlike analytic part, such results as coefficient inequalities, an integral representation, a growth theorem, an…

Almost automorphy in the context of hyperfunctions is the main aim of this work. We give different equivalent definitions of almost automorphic hyperfunctions and then we study this class of hyperfunctions.

We develop new elements of harmonic analysis on the complex sphere on the basis of which Bernstein's, Jackson's and Kolmogorov's inequalities are established. We apply these results to get order sharp estimates of $m$-term approximations.…

In this paper, we analyze various classes of multi-dimensional $\rho$-almost periodic type functions $F : I \times X \rightarrow Y$ and multi-dimensional $(\omega,\rho)$-almost periodic type functions $F : I \times X \rightarrow Y,$ where…

In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…

We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…

In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information…

Uniqueness theorems are considered for various types of almost periodic objects: functions, measures, distributions, multisets, holomorphic and meromorphic functions.

We prove that Besicovitch almost periodic multivalued maps ${\bf R}\ni t \to F(t) \in cl U$ have Besicovitch almost periodic selections, where $cl U$ is the collection of non-empty closed sets of a complete metric space $U$.

The article is devoted to holomorphic and meromorphic functions of quaternion and octonion variables. New classes of quasi-conformal and quasi-meromorphic mappings are defined and investigated. Properties of such functions such as their…

The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and…