Quasigroups, association schemes, and Laplace operators on almost periodic functions. (English) Zbl 0671.43009
Algebraic, extremal and metric combinatorics, Pap. Conf., Montreal/Can. 1986, Lond. Math. Soc. Lect. Note Ser. 131, 205-218 (1988).
[For the entire collection see Zbl 0655.00008.]
The association scheme determined by a finite non-empty quasigroup furnishes generalized Laplace operators \(\Delta_ i\) on the space of almost periodic functions on the free group that is the universal multiplication group of the quasigroup. In this paper the author proves an existence theorem for solutions of the equation \(\Delta_ iu=0\) on the closed convex hull of the set of twisted translates of an given almost periodic function f. This theorem generalizes the classical result on the existence of von Neumann means of almost periodic functions.
The association scheme determined by a finite non-empty quasigroup furnishes generalized Laplace operators \(\Delta_ i\) on the space of almost periodic functions on the free group that is the universal multiplication group of the quasigroup. In this paper the author proves an existence theorem for solutions of the equation \(\Delta_ iu=0\) on the closed convex hull of the set of twisted translates of an given almost periodic function f. This theorem generalizes the classical result on the existence of von Neumann means of almost periodic functions.
Reviewer: C.Pereira da Silva
MSC:
| 43A60 | Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions |
| 20N05 | Loops, quasigroups |
| 43A07 | Means on groups, semigroups, etc.; amenable groups |
