Power Bounded Matrices of Fourier-Stieltjes Transforms.

Bounded Functions and Fourier Transforms

1. Statement of the principal result. The class of sequences obtainable as Fourier coefficients of measures on the circle group presents numerous structure problems of interest. Amongst the earliest results somewhat akin to that stated below appear Banach's theorems about lacunary coefficients; see e.g., [4, pp. 215-220]. More recently Helson [3] has studied analogous questions when the group c...

Representation of Functions as Absolutely Convergent Fourier-stieltjes Transforms

0. Introduction. Let G be a locally compact Abelian group, and G* its group of (continuous) characters. We write (y, x) to indicate the function on G*XG which is the value of the character y EG* at the point *6G, or, dually, the value of the character xEG at the point y EG*. Borel sets in G are taken to be the smallest cr-algebra of sets containing all closed sets. We consider the set of all re...

SPECTRUM OF THE FOURIER-STIELTJES ALGEBRA OF A SEMIGROUP

For a unital foundation topological *-semigroup S whose representations separate points of S, we show that the spectrum of the Fourier-Stieltjes algebra B(S) is a compact semitopological semigroup. We also calculate B(S) for several examples of S.

A note on power bounded matrices

Ela a Note on Power Bounded Matrices

We say A is convergent to the matrix X = [xij ] if the sequences (A )ij converge to xij as k → ∞. A matrix is convergent if it is convergent to some matrix. This is a special case of convergence as defined in [4, Definition 10.1], for the matrix sequence {A,A, A, . . . }. In particular, we say A is zero convergent when A is convergent to the zero matrix. We distinguish between convergence and z...