M. Langer

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Articles: 2

Stability of N-extremal measures

Matthias Langer, Harald Woracek

↓ Abstract   |   Article (.pdf)

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

Heinz Langer, Matthias Langer, Zoltán Sasvári

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

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