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A representation formula for slice regular functions over slice-cones in several variables
The aim of this paper is to extend the so called slice analysis to a general case in which the codomain is a real vector space of even dimension,...
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Dilation Theory in Several Variables—The Symmetrized Bidisc
This chapter deals with the highly successful theory of dilation on the symmetrized bidisc. This involves the joint spectrum which we begin with. We...
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On Lappan’s Five-Valued Theorem for φ-Normal Functions of Several Variables
Let 𝕌 m ⊂ ℂ m be a unit ball centered at the origin and let ℙ n be an n -dimensional complex projective space with the metric E ℙ n . Moreover, let φ : [0 , ...
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Some Results Regarding Partial Differential Polynomials and the Uniqueness of Meromorphic Functions in Several Variables
In this paper, we mainly investigate the value distribution of meromorphic functions in ℂ m with its partial differential and uniqueness problem on...
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Dilation Theory in Several Variables—The Euclidean Ball
We continue the study of dilation of a tuple. Now, we have a contractive tuple. The dilation theory involves the full Fock space in the non-commuting...
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Value distribution of q-differences of meromorphic functions in several complex variables
In this paper, we study q -difference analogues of several central results in value distribution theory of several complex variables such as q -differen...
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Random Variables
Random variables are the central objects of study in probability. The name ‘random variables’ is somewhat of a misnomer since they are neither random...
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Entire solutions for several second-order partial differential-difference equations of Fermat type with two complex variables
This paper is concerned with description of the existence and the forms of entire solutions of several second-order partial differential-difference...
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Components of the Space of Weighted Composition Operators Between Different Fock Spaces in Several Variables
In this paper, we completely solve the topological structure problem for the space of nonzero weighted composition operators acting between Fock...
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On the Coefficient Inequalities for a Class of Holomorphic Map**s Associated with Spirallike Map**s in Several Complex Variables
In this paper, we establish the Fekete and Szegö inequality for a class of holomorphic functions related to the class of normalized spirallike...
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Complex Numbers and Complex Plane
In this chapter we recall some concepts from basic courses in mathematical analysis of real-valued functions of one and several variables as well as...
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Asymptotics of the Solution to the Cauchy Problem for a Singularly Perturbed Operator Differential Transport Equation in Several Space Variables
AbstractA formal asymptotic expansion of the solution to the Cauchy problem for a singularly perturbed operator differential transport equation in...
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Comparison of Clark Measures in Several Complex Variables
Let \(\mathbb {D}\) denote the unit disc of...
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Characterizations of Herglotz–Nevanlinna Functions Using Positive Semi-Definite Functions and the Nevanlinna Kernel in Several Variables
In this paper, we give several characterizations of Herglotz–Nevanlinna functions in terms of a specific type of positive semi-definite functions...
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Mahler Measures of Polynomials in Several Variables
We discuss the Mahler measure of polynomials in any number of variables, including Boyd’s Conjecture that the set...
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Measurable Functions and Random Variables
To study random variable in a more general setting, we introduce the notion of measurable functions. In probability theory, a random variable is a...
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Modes of convergence of random variables and algebraic genericity
Important probabilistic problems require to find the limit of a sequence of random variables. However, this limit can be understood in different ways...
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Sums of Independent Random Variables
In this chapter we collect basic definitions and results on the normal approximation of distributions of independent random variables (in Kolmogorov...