Spaces of generalized functions of finite variation

Author: Ani Ozbetelashvili
Co-authors: Ani Ozbetelashvili
Keywords: Generalized finite variation functions, variable exponential variation
Annotation:

The article is of a research nature and represents, according to Wiener, the classification of the class of functions of finite variations, when the exponent is a non-constant function. It has been shown that this class can be defined even when the exponent is essentially an undefined function, in contrast to the variable introduced by a similar class introduced by Castillo, Morientes and Rafiero, which is defined only by bounded exponents. It is also shown that the new class is not much smaller than the class of Castillo, Morientes and Rafiero, with a constructed bounded exponent, for which the class of Castillo Morientes and Rafiero is its own subset of the newly defined class of functions. It is shown that this class does not represent the bunch function space according to Bennett and Sharpell. Some interesting features of the newly introduced class have also been identified.

Lecture files:

განზოგადებული სასრული ვარიაციის ფუნქციათა სივრცეების შესახებ [ka]