# M. Langer

orcid.org/0000-0001-8813-7914
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Articles: 2

### Stability of N-extremal measures

Methods Funct. Anal. Topology 21 (2015), no. 1, 69-75

A positive Borel measure $\mu$ on $\mathbb R$, which possesses all power moments, is N-extremal if the space of all polynomials is dense in $L^2(\mu)$. If, in addition, $\mu$ generates an indeterminate Hamburger moment problem, then it is discrete. It is known that the class of N-extremal measures that generate an indeterminate moment problem is preserved when a finite number of mass points are moved (not removed''!). We show that this class is preserved even under change of infinitely many mass points if the perturbations are asymptotically small. Thereby asymptotically small'' is understood relative to the distribution of ${\rm supp}\mu$; for example, if ${\rm supp}\mu=\{n^\sigma\log n:\,n\in\mathbb N\}$ with some $\sigma>2$, then shifts of mass points behaving asymptotically like, e.g. $n^{\sigma-2}[\log\log n]^{-2}$ are permitted.

### Continuations of Hermitian indefinite functions and corresponding canonical systems: an example

Methods Funct. Anal. Topology 10 (2004), no. 1, 39-53