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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4412

Title: Extremal products in Bombieri's norm
Authors: Beauzamy, Bernard
Issue Date: 1996
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Citation: Bernard Beauzamy, "Extremal products in Bombieri's norm", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 28 (1996) suppl., pp. 73-89.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
28 (1996) s.
Abstract: Let P be a homogeneous polynomial in any number of variables, of any degree, with complex coefficients. We give a complete description of the Q's, of all degrees, such that [Q] = 1 and [PQ] is either maaimal or minimal, where $[\cdot]$ is Bombieri's norm. Far this, we introduce a matrix, built with partial derivatives of P; the quantity [PQ] appears as the l2 norm of the product of this matrix by a vector column associated with Q: thus products of polynomials are replaced by the product of a matrix by a vector, a mach simpler feature. The extreme values of [PQ] are eigenvalues of this matrix. As an application, we give an exact estimate of the norm of the differential operator P(D).
URI: http://hdl.handle.net/10077/4412
ISSN: 0049-4704
Appears in Collections:Rendiconti dell‘ Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.28 (1996) s.

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