Related papers: Hyperholomorphic functions on commutative algebras
We establish a general uniqueness theorem for subharmonic functions of several variables on a domain. A corollary from this uniqueness theorem for holomorphic functions is formulated in terms of the zero subset of holomorphic functions and…
This article serves as an introduction to several recent developments in the study of quasisymmetric functions. The focus of this survey is on connections between quasisymmetric functions and the combinatorial Hopf algebra of noncommutative…
The article is devoted to investigation of classes of functions monotone as functions on general $C^*$-algebras that are not necessarily the $C^*$-algebras of all bounded linear operators on a Hilbert space as it is in classical case of…
In this paper we introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy many of their important properties.…
This set of lecture notes gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations. Later sections describe more advanced…
We give necessary and sufficient condition so that we have d-hypercyclicity for operators who map a holomorphic function to a partial sum of the Taylor expansion. This problem is connected with doubly universal Taylors series and this is an…
Biunivalent holomorphic functions form an interesting class in geometric function theory and are connected with special functions and solutions of complex differential equations. The paper reveals a deep connection between biunivalence and…
In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of…
We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…
We study finite energy classes of quasiplurisubharmonic (qpsh) functions in the setting of toric compact K{\"a}hler manifolds. We characterize toric qpsh functions and give necessary and sufficient conditions for them to have finite…
The $q$-Whittaker function $W_\lambda(\mathbf{x};q)$ associated to a partition $\lambda$ is a $q$-analogue of the Schur function $s_\lambda(\mathbf{x})$, and is defined as the $t=0$ specialization of the Macdonald polynomial…
We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…
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.
We generalize and complete some of Maxim's recent results on Alexander invariants of a polynomial transversal to the hyperplane at infinity. Roughly speaking, and surprisingly, such a polynomial behaves both topologically and algebraically…
C*-algebras generalizing Cuntz-Krieger algebras can be associated to hyperbolic homeomorphisms of compact metric spaces. They satisfy a non-commutative form of Spanier-Whitehead duality with respect to K-theory. We prove this for the case…
In this paper we investigated holomorphic functions (belonging to the kernel of the Dirac operator) in Cayley-Dickson algebras. For this purpose, we study the structure of Cayley-Dickson algebras. We also provide an algorithm for the…
We define finite field $A$-hypergeometric functions and show that they are Fourier expansions of families of exponential sums on the torus. For an appropriate choice of $A$, our finite field $A$-hypergeometric function can be specialized to…
As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.
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…
In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic…