Elliptic distances in Hilbert spaces

Abstract

Let X be a pre-Hilbert space of dimension at least 2 and define X 0 := X\{0}. In Theorems 1 and 2 we determine all f : X 0 → X 0 satisfying the functional equation

Pseudo-cohomology of general extensions

“…(iii) The discussions in this section hold good on any pre-Hilbert space with respect to Lorentz-Minkowski distance [2].…”