In this paper, we generalize the definition of fuzzy inner product space that is introduced by Lorena Popa and Lavinia Sida on a complex linear space. Certain properties generalized function are shown. Furthermore, prove produces Nadaban-Dzitac norm. Finally, concept orthogonality given some its proven.

Solitons in classical field theories correspond to states quantum theories. If the spatial dimension is infinite, then momentum eigenstates are not normalizable. This leads infrared divergences, which generally regularized via wave packets or by compactification. However, some applications both possibilities undesirable. In present note, we introduce a finite inner product on translation-invari...

In this paper, we introduce an inner product on abelian groups and, after investigating the basic properties of product, first show that each group is a torsion-free normed group. We give examples such and describe norms induced by products. Among other results, Hilbert groups, midconvex orthogonal subgroups are presented, Riesz representation theorem divisible proved.