Related papers: Functions of a Single Variable
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
The study of essential and strongly essential variables in functions defined on finite sets is a part of $k$-valued logic. We extend the main definitions from functions to terms. This allows us to apply concepts and results of Universal…
We develop Cresson's nondifferentiable calculus of variations on the space of H\"{o}lder functions. Several quantum variational problems are considered: with and without constraints, with one and more than one independent variable, of first…
Under certain initial conditions, we prove the existence of set-valued selectors of univariate compact-valued multifunctions of bounded (Jordan) variation when the notion of variation is defined taking into account only the Pompeiu…
The theory of slice regular functions of a quaternionic variable, introduced in 2006 by Gentili and Struppa, extends the notion of holomorphic function to the quaternionic setting. This fast growing theory is already rich of many results…
The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of functions of bounded variation and of Sobolev functions on…
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…
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…
Within the geometrical framework developed in arXiv:0705.2362, the problem of minimality for constrained calculus of variations is analysed among the class of differentiable curves. A fully covariant representation of the second variation…
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 paper we determine the region of variability for spirallike funcions with respect to a boundary point. In the final section we graphically illustrate the region of variability for several sets of parameters.
In this paper, we study functions of bounded variation on a complete and connected metric space with finite one-dimensional Hausdorff measure. The definition of BV functions on a compact interval based on pointwise variation is extended to…
In this paper we develop with considerable details a theory of multivector functions of a $p$-vector variable. The concepts of limit, continuity and differentiability are rigorously studied. Several important types of derivatives for these…
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…
This book considers posing and the methods of solving simple linear boundary-value problems in classical mathematical physics. The questions encompassed include: the fundamentals of calculus of variations; one-dimensional boundary-value…
The paper introduces a new concept of $\Lambda $-variation of multivariable functions and investigates its connection with the convergence of multidimensional Fourier series
This paper is devoted to investigating the sequence of some linear functionals in the space $BV$ of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In…
We generalize the classical calculus rules satisfied by functions of bounded variation to the framework of RCD spaces. In the infinite dimensional setting we are able to define an analogue of the distributional differential and on finite…
In the preceding articles we considered fractional integral transforms involving one real scalar variable, one real matrix variable and real scalar multivariable case. In the present paper we consider the multivariable case when the…
Notions of a "holomorphic" function theory for functions of a split-quaternionic variable have been of recent interest. We describe two found in the literature and show that one notion encompasses a small class of functions, while the other…