Interpolation sets for Fréchet measures
We introduce various classes of interpolation sets for Fréchet measures-the measure-theoretic analogues of bounded multilinear forms on products of C(K) spaces.
We introduce various classes of interpolation sets for Fréchet measures-the measure-theoretic analogues of bounded multilinear forms on products of C(K) spaces.
A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case.
2000 Mathematics Subject Classification: Primary 43A22, 43A25.We prove a representation theorem for bounded operators commuting with translations on L2ω(G,H), where G is a locally compact abelian group, H is a Hilbert space and ω is a weight on G. Moreover, in the particular case when G = R, we characterize completely the spectrum of the shift operator S1,ω on Lω2(R,H).