Weighted polynomial approximation of entire functions, II
نویسندگان
چکیده
منابع مشابه
Coupled systems of equations with entire and polynomial functions
We consider the coupled system$F(x,y)=G(x,y)=0$,where$$F(x, y)=bs 0 {m_1} A_k(y)x^{m_1-k}mbox{ and } G(x, y)=bs 0 {m_2} B_k(y)x^{m_2-k}$$with entire functions $A_k(y), B_k(y)$.We derive a priory estimates for the sums of the rootsof the considered system andfor the counting function of roots.
متن کاملPolynomial Approximation of Functions
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hubert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer o...
متن کاملDivision of Entire Functions by Polynomial Ideals
In [ASTW] it was given a Grobner reduction based division formula for entire functions by polynomial ideals. Here we give degree bounds where the input function can be truncated in order to compute approximations of the coe cients of the power series appearing in the division formula within a given precision. In addition, this method can be applied to the approximation of the value of the rema...
متن کاملcoupled systems of equations with entire and polynomial functions
we consider the coupled system$f(x,y)=g(x,y)=0$,where$$f(x, y)=bs 0 {m_1} a_k(y)x^{m_1-k}mbox{ and } g(x, y)=bs 0 {m_2} b_k(y)x^{m_2-k}$$with entire functions $a_k(y), b_k(y)$.we derive a priory estimates for the sums of the rootsof the considered system andfor the counting function of roots.
متن کاملBest Polynomial Approximation in L-Norm and (p, q)-Growth of Entire Functions
and Applied Analysis 3 which vanishes on K except perhaps for a pluripolar subset and satisfies the complex Monge-Ampère equation (see [12]): (dd c V K ) n = 0 on Cn \ K. (16) If n = 1, the Monge-Ampère equation reduces to the classical Laplace equation. For this reason, the functionV K is considered as a natural counterpart of the classical Green function with logarithmic pole at infinity and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1981
ISSN: 0021-9045
DOI: 10.1016/0021-9045(81)90089-7