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Classification theorems for operators preserving zeros in a strip
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2017 (English)In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 132, no 1, p. 177-215Article in journal (Refereed) Published
Abstract [en]

We characterize all linear operators which preserve certain spaces of entire functions whose zeros lie in a closed strip. Necessary and sufficient conditions are obtained for the related problem with real entire functions, and some classical theorems of de Bruijn and Pólya are extended. Specifically, we reveal new differential operators which map real entire functions whose zeros lie in a strip to real entire functions whose zeros lie in a narrower strip; this is one of the properties that characterize a “strong universal factor” as defined by de Bruijn. Using elementary methods, we prove a theorem of de Bruijn and extend a theorem of de Bruijn and Ilieff which states a sufficient condition for a function to have a Fourier transform with only real zeros.

Place, publisher, year, edition, pages
Springer New York LLC , 2017. Vol. 132, no 1, p. 177-215
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-216471DOI: 10.1007/s11854-017-0018-3ISI: 000404532200007Scopus ID: 2-s2.0-85021430862OAI: oai:DiVA.org:kth-216471DiVA, id: diva2:1162031
Note

QC 20171201

Available from: 2017-12-01 Created: 2017-12-01 Last updated: 2017-12-01Bibliographically approved

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