ABSTRACT: This paper investigates four classes of functions with a single discontinuous point. We give the sufficient and necessary conditions under which the second order iterates are continuous ...

Abstract: Paper is devoted to the development of a method for approximating discontinuous functions by discontinuous splines and the construction of an algorithm for detecting discontinuity lines. The ...

There are many scientific problems related to the topic of interpolation, especially for non-‎continuous functions, as well as the evaluating of the integrals of such non-continuous ‎‎functions. These ...

For nonparametric regression, where the regression function has discontinuity points, the kernel regression estimator and cross-validation are known to be affected by ...

The present paper is devoted to the investigation of the properties of the space of distributions with discontinuous test functions of several variables. The consideration of discontinuous test ...

ABSTRACT: In this paper we embark on the study of Dynamic Systems of Shifts in the space of piece-wise continuous functions analogue to the known Bebutov system. We give a formal definition of a ...

This example illustrates some properties of splines. Splines are curves, which are usually required to be continuous and smooth. Splines are usually defined as piecewise polynomials of degree n with ...