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Polya-Schur master theorems for circular domains and their boundaries
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-1055-1474
2009 (English)In: Annals of Mathematics, ISSN 0003-486X, E-ISSN 1939-8980, Vol. 170, no 1, 465-492 p.Article in journal (Refereed) Published
Abstract [en]

We characterize all linear operators on finite or infinite-dimensional polynomial spaces that preserve the property of having the zero set inside a prescribed region Omega subset of C for arbitrary closed circular domains Omega (i.e., images of the closed unit disk under a Mobius transformation) and their boundaries. This provides a natural framework for dealing with several long-standing fundamental problems, which we solve in a unified way. In particular, for Omega = R our results settle open questions that go back to Laguerre and Polya-Schur.

Place, publisher, year, edition, pages
2009. Vol. 170, no 1, 465-492 p.
Keyword [en]
transformed polynomials, linear transformations, multiplier sequences, algebraic equations, zeros, operators
National Category
URN: urn:nbn:se:kth:diva-18800DOI: 10.4007/annals.2009.170.465ISI: 000270236000014ScopusID: 2-s2.0-71449101577OAI: diva2:336847

QC 20100525

Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2014-10-09Bibliographically approved

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