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Extremal products in Bombieri's norm
Beauzamy, Bernard
1996
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).
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
28 (1996) s.
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
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.
Languages
en
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