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 Hp 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.

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