The complex moment problem: determinacy and extendibility

Determinacy of a Rational Moment Problem

Relational Quantum Mechanics and the Determinacy Problem∗

Quantum mechanics describes certain systems as being in superpositions of their properties, yet every measurement on every system that we are able to perform yields a determinate result. The “orthodox” formulation of the theory builds this in by including a postulate that such superpositions “collapse” at the time of measurement. This strategy fails to really explain why such measurements are d...

Subdivision Extendibility

Let H be a multigraph and G a graph containing a subgraph isomorphic to a subdivision of H, with S ⊂ V (G) (the ground set) the image of V (H) under the isomorphism. We consider connectivity and minimum degree or degree sum conditions sufficient to imply there is a spanning subgraph of G isomorphic to a subdivision of H on the same ground set. These results generalize a number of theorems in th...

On the determinacy of complex Jacobi matrices

The aim of this paper is to explore to which extend the theory of the Hamburger moment problem for real Jacobi matrices generalizes to the case of complex Jacobi matrices. In particular, we characterize the indeterminacy in terms of uniqueness of closed extensions of Jacobi matrices, and discuss the link to the growth of the smallest singular values of the underlying Hankel matrices. As a bypro...

The Complexity of the Extendibility Problem for Finite Posets

For a finite poset P let EXT(P ) denote the following decision problem. Given a finite poset Q and a partial map f from Q to P , decide whether f extends to a monotone total map from Q to P . It is easy to see that EXT(P ) is in the complexity class NP. In [SIAM J. Comput., 28 (1998), pp. 57–104], Feder and Vardi define the classes of width 1 and of bounded strict width constraint satisfaction ...