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.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1027–1045, August, 1998.
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Bushev, D.M. Isometry of functional spaces with different number of variables. Ukr Math J 50, 1170–1191 (1998). https://doi.org/10.1007/BF02513090
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DOI: https://doi.org/10.1007/BF02513090