منابع مشابه
Waring’s Problem for Polynomials in Two Variables
We prove that all polynomials in several variables can be decomposed as the sums of kth powers: P (x1, . . . , xn) = Q1(x1, . . . , xn) + · · ·+Qs(x1, . . . , xn), provided that elements of the base field are themselves sums of kth powers. We also give bounds for the number of terms s and the degree of the Qi . We then improve these bounds in the case of two variables polynomials of large degre...
متن کاملWaring Problem for Polynomials in Two Variables
We prove that all polynomials in several variables can be decomposed as the sum of kth powers: P (x1, . . . , xn) = Q1(x1, . . . , xn) + · · ·+Qs(x1, . . . , xn), provided that elements of the base field are themselves sum of kth powers. We also give bounds for the number of terms s and the degree of the Qi . We then improve these bounds in the case of two variables polynomials to get a decompo...
متن کاملOn Pseudo Hermite Matrix Polynomials of Two Variables
Abstract. The main aim of this paper is to define a new polynomial, say, pseudo hyperbolic matrix functions, pseudo Hermite matrix polynomials and to study their properties. Some formulas related to an explicit representation, matrix recurrence relations are deduced, differential equations satisfied by them is presented, and the important role played in such a context by pseudo Hermite matrix p...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1996
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1996.176.297