Related papers: Functions of a Single Variable
Certain relations between the Fourier transform of a function of bounded variation and the Hilbert transform of its derivative are revealed. The widest subspaces of the space of functions of bounded variation are indicated in which the…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
In this paper, we introduce and investigate a novel class of analytic and univalent functions of negative coefficients in the open unit disk. For this function class, we obtain characterization and distortion theorems as well as the radii…
Invariant functions and metrics are studied on various classes of domains in $\Bbb C^n.$
In this article, we determine conditions on the parameters of a generalized convolution operator such that it belongs to the Hardy space and to the space of bounded analytic functions. Results obtained are new and their usefulness is…
The aim of this paper is to define a new operator by using the generalized Struve functions. By using this operator we define a subclass of analytic functions. We discuss some properties of this class such as inclusion problems, radius…
The abundance of functional observations in scientific endeavors has led to a significant development in tools for functional data analysis (FDA). This kind of data comes with several challenges: infinite-dimensionality of function spaces,…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
Recent innovations in the differential calculus for functions of non-commuting variables, beginning with a quaternionic variable, are now extended to consider some integration.
We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of…
In this paper, we introduce concepts of separable functions in balls and in the whole space, and develop a new method to investigate the qualitative properties of separable functions. We first study the axial symmetry and monotonicity of…
This paper is part of series on self-contained papers in which a large part, if not the full extent, of the asymptotic limit theory of summands of independent random variables is exposed. Each paper of the series may be taken as review…
This is the first part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. We prove two main results concerning systems that are regular singular at…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
Statisticians usually restrict regression to model relationships that are explicitly defined dependent and independent random variables; this paper outlines the newly developed method of non-response analysis and rotational analysis for…
Expansion of real numbers is a basic research topic in number theory. Usually we expand real numbers in one given base. In this paper, we begin to systematically study expansions in multiple given bases in a reasonable way, which is a…
In this article, we further explore convex functions by revealing new bounds, resulting from stronger convexity behavior. In particular, we define the so called radical convex functions and study their properties. We will see that such…
We study polynomials with no zeros on the unit ball in complex Euclidean space with a view toward characterizing when a rational function is bounded on the ball. We give a complete local description of such polynomials in two variables near…
Classical theorem of Luzin states that a measurable function of one real variable is "almost" continuous. For measurable functions of several variables the analogous statement (continuity on the product of sets having almost full measure)…
We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…