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Lower bounds for polynomials of a quaternionic variable

Authors: Graziano Gentili and Daniele C. Struppa
Journal: Proc. Amer. Math. Soc. 140 (2012), 1659-1668
MSC (2010): Primary 30G35, 30C10
Published electronically: August 24, 2011
MathSciNet review: 2869150
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Abstract: We prove an analog of the Ehrenpreis-Malgrange Lemma for polynomials with quaternionic coefficients, and we apply it to obtain a bound on the growth of the quotient between a slice regular function and a quaternionic polynomial.

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Additional Information

Graziano Gentili
Affiliation: Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy

Daniele C. Struppa
Affiliation: Schmid College of Science and Technology, Chapman University, Orange, California 92866

Received by editor(s): November 8, 2010
Received by editor(s) in revised form: January 13, 2011
Published electronically: August 24, 2011
Additional Notes: The authors express their gratitude to Chapman University for its partial support of this project
The first author acknowledges the support of G.N.S.A.G.A. of INdAM and MIUR (Research Project “Proprietà geometriche delle varietà reali e complesse”)
Dedicated: Dedicated to the memory of Professor Leon Ehrenpreis, 1930-2010
Communicated by: Franc Forstneric
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.