Quadratic Functional Equation and Inner Product Spaces
Copyright policy )Quadratic Functional Equation and Inner Product Spaces
The aim of the paper is to characterize inner product spaces as those in which the square of the norm satisfies some functional equations. The author considers five such equations. Actually, the equations are solved in general, and in some important cases it is noticed that their only solutions are quadratic functionals (i.e. functionals satisfying the Jordan-von Neumann identity).
- University of Waterloo Canada
Functional equations for real functions, inner product spaces, Jordan-von Neumann identity, functional equations, Functional equations for functions with more general domains and/or ranges, characterization, quadratic functionals, Quadratic and bilinear forms, inner products
Functional equations for real functions, inner product spaces, Jordan-von Neumann identity, functional equations, Functional equations for functions with more general domains and/or ranges, characterization, quadratic functionals, Quadratic and bilinear forms, inner products
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).128 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 1% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!