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.
Lower bounds for polynomials of a quaternionic variable / Gentili, Graziano; Struppa, Daniele C.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 140:(2012), pp. 1659-1668. [10.1090/S0002-9939-2011-11027-X]
Lower bounds for polynomials of a quaternionic variable
GENTILI, GRAZIANO;
2012
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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