KENT AND KLEEMEIER AWARD LECTURES
نویسندگان
چکیده
منابع مشابه
Topics in entire functions . Lectures in Kent University
Theorem. This class is closed under differentiation. Proof. Let d = degP . Then degP ′ = d−1, so P ′ has at most d−1 zeros (counting multiplicity). On the other hand, it follows from Rolle’s theorem that P ′ has at least d − 1 real zeros (counting multiplicity!). So all zeros of P ′ are real. This is a non-trivial proof! We used the following principle: if X ⊂ Y are finite subsets, and cardX ≥ ...
متن کاملTopics in entire functions . Lectures in Kent University A . Eremenko
Theorem. This class is closed under differentiation. Proof. Let d = degP . Then degP ′ = d−1, so P ′ has at most d−1 zeros (counting multiplicity). On the other hand, it follows from Rolle’s theorem that P ′ has at least d − 1 real zeros (counting multiplicity!). So all zeros of P ′ are real. This is a non-trivial proof! We used the following principle: if X ⊂ Y are finite subsets, and cardX ≥ ...
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ژورنال
عنوان ژورنال: Innovation in Aging
سال: 2019
ISSN: 2399-5300
DOI: 10.1093/geroni/igz038.2229