The generalized degree symmetric moment problem

The full moment problem on subsets of probabilities and point configurations

“…A general treatment of the full ∞−KMP has been given e.g. in [1], [3, Chapter 5, Section 2], [6], [8], [16], [17], [18], [19], [42,Section 12.5], [44]. Special infinite dimensional supports, particularly useful in applications, have been considered e.g.…”

“…In Section 1, we introduce some basic notions and formulate the KMP for K ⊆ D ′ (R d ). In Subsection 2.1 we recall our previous result in [20], which combines techniques from the finite and the infinite dimensional moment theory (see reference therein), in particular [3], [6], [34] and [43]. The case where K is the space of sub-probabilities is treated in Subsection 2.2.…”

On the complex moment problem

“…For the beginning we consider (1.1) in the case m, n ∈ N 0 and dρ(z) defined on C. The second part of the article (Subsection 4) will be devoted to the interesting for mathematical physic infinite-dimensional generalization of such theory, where in the integral (1.1) we change C to a complex nuclear space. Such transfer from the one-dimensional to the infinite-dimensional case is analog to the case of the classical (real) moment problem, see [4,5,7]. Our approach is based on the generalization [3] of the method, which goes back to the works of M. G. Krein [17,18].…”

Stochastic and Infinite Dimensional Analysis

“…[8, Vol. II, Theorem 2.1] and [9]). Before stating the theorem, we need some preliminary considerations.…”

“…In fact, several infinite-dimensional moment problems have been investigated using the theory of generalized eigenfunction expansion for self-adjoint operators (see e.g. [4,5,7,8,9,35,57]). This approach is well developed for nuclear spaces in [5,Chapter 8] and [8, Vol.…”