Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 3, pp. 413--418

THE SMIRNOV CLASS ON COMPACT GROUPS WITH ORDERED DUALS

By

HENRY HELSON, * University of California, Berkeley*

*SUMMARY. *On the circle group, the Smirnov
class *A* is the largest extension of the spaces *H*^{p} to
which the calculus of Fourier series can be extended (Helson,
1990a,b,c). This note explores a definition of the class on the
compact abelian groups studied in Helson, (1975).

*AMS (1991) subject classification. * Primary 43A17; secondary
30D55.

*Key words and phrases. * Smirnov class, compact
groups with ordered duals, generalized function theory.