Karim Kellay

Binomial sums, moments and invariant subspaces

AbstractThe main result of this paper is that if a sequence of complex numbers (an)n≥0 satisfiesn

Havin-Mazya type uniqueness theorem for Dirichlet spaces

sumlimits_{mathop {k = 0}limits_{k even} }^n {left({_k^n } right)a_k = O(n^r)}

A Primer on the Dirichlet Space: Hardy spaces

nand % MathType!MTEF!2!1!+-n

A Primer on the Dirichlet Space: References

sumlimits_{mathop {k = 0}limits_{k odd} }^n {left({_k^n } right)a_k = O(n^r )} as n to infty,

A Primer on the Dirichlet Space: Invariant subspaces

n for some integerr≥0, thenan=0 for alln>r. As an application, we deduce a localized form of a theorem of Allan about nilpotent elements in Banach algebras, and this in turn leads to an invariant-subspace theorem. As a further application, we prove a variant of Carlemans theorem on the unique determination of probability distributions by their moments. The paper concludes with a quantitative form of the main result.