منابع مشابه
Polynomial interpolation in several variables
This is a survey of the main results on multivariate polynomial interpolation in the last twenty five years, a period of time when the subject experienced its most rapid development. The problem is considered from two different points of view: the construction of data points which allow unique interpolation for given interpolation spaces as well as the converse. In addition, one section is devo...
متن کاملPolynomial interpolation in several variables
1 0. PREAMBLE I want to thank the organizers for inviting me to this meeting as it gives me the opportunity to help celebrate Sam Conte who gave me my rst academic job. More than that, he provided my children with many years of summer camp in the wilds of New Hampshire and Wisconsin, and at least two of them think that those summers in New Hampshire were essential for their growing up (and I te...
متن کاملSpectral Lifting in Banach Algebras and Interpolation in Several Variables
Let A be a unital Banach algebra and let J be a closed two-sided ideal of A. We prove that if any invertible element of A/J has an invertible lifting in A, then the quotient homomorphism Φ : A → A/J is a spectral interpolant. This result is used to obtain a noncommutative multivariable analogue of the spectral commutant lifting theorem of Bercovici, Foiaş, and Tannenbaum. This yields spectral v...
متن کاملAlgebraic Aspects of Polynomial Interpolation in Several Variables
This paper summarizes relations between the constructive theory of polynomial ideals and polynomial interpolation in several variables. The main ingredient is a generalization of the algorithm for division with remainder to \quotients" of polynomials and nite sets of polynomi-als. x1. Introduction When compared to the univariate case, polynomial interpolation in several variables turns out to b...
متن کاملPolynomial interpolation in several variables: lattices, differences, and ideals
When passing from one to several variables, the nature and structure of polynomial interpolation changes completely: the solvability of the interpolation problem with respect to a given finite dimensional polynomial space, like all polynomials of at most a certain total degree, depends not only on the number, but significantly on the geometry of the nodes. Thus the construction of interpolation...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2013
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2013-11571-6