Extension of Characters on *-Semigroups.
Characterization of perfect involution groups.
Erratum: On the positive definiteness of n (a sequence of exponentials).
On the positive definiteness of n (a sequence of exponentials).
We find sharp asymptotic estimates for a sequence of exponentials to define a positive definite bilinear form.
Semiperfect countable C-separative C-finite semigroups.
Semiperfect semigroups are abelian involution semigroups on which every positive semidefinite function admits a disintegration as an integral of hermitian multiplicative functions. Famous early instances are the group on integers (Herglotz Theorem) and the semigroup of nonnegative integers (Hamburger's Theorem). In the present paper, semiperfect semigroups are characterized within a certain class of semigroups. The paper ends with a necessary condition for the semiperfectness of a finitely generated...
Extreme positive definite double sequences which are not moment sequences.
From the fact that the two-dimensional moment problem is not always solvable, we can deduce that there must be extreme ray generators of the cone of positive definite double sequences which are nor moment sequences. Such an argument does not lead to specific examples. In this paper it is shown how specific examples can be constructed if one is given an example of an N-extremal indeterminate measure in the one-dimensional moment problem (such examples exist in the literature). Konrad Schmüdgen had...
Characterization of moment multisequences by a variation of positive definiteness.
On the Stieltjes moment problem on semigroups
We characterize finitely generated abelian semigroups such that every completely positive definite function (a function all of whose shifts are positive definite) is an integral of nonnegative miltiplicative real-valued functions (called nonnegative characters).
An example of a positive semidefinite double sequence which is not a moment sequence
The first explicit example of a positive semidefinite double sequence which is not a moment sequence was given by Friedrich. We present an example with a simpler definition and more moderate growth as .
Stieltjes perfect semigroups are perfect
An abelian -semigroup is perfect (resp. Stieltjes perfect) if every positive definite (resp. completely so) function on admits a unique disintegration as an integral of hermitian multiplicative functions (resp. nonnegative such). We prove that every Stieltjes perfect semigroup is perfect. The converse has been known for semigroups with neutral element, but is here shown to be not true in general. We prove that an abelian -semigroup is perfect if for each there exist and such that ...
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