Isometry of functional spaces with different number of variables

Abstract

We construct spaces of real functions of n + k variables that are isometric to spaces of real functions given on an n-dimensional Euclidean space. We present certain properties and examples of delta-like kernels used for the construction of isometric spaces of functions with different number of variables. We prove certain assertions that enable one to construct delta-like kernels with many variables by using delta-like kernels with smaller number of variables.