Polynomial approximation in several variables
نویسندگان
چکیده
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...
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We obtain L decay estimates in λ for oscillatory integral operators Tλ whose phase functions are homogeneous polynomials of degree m and satisfy various genericity assumptions. The decay rates obtained are optimal in the case of (2+2)–dimensions for any m, while in higher dimensions the result is sharp for m sufficiently large. The proof for large m follows from essentially algebraic considerat...
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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: Journal of Approximation Theory
سال: 2020
ISSN: 0021-9045
DOI: 10.1016/j.jat.2019.105364