Functions of exponential type and the cardinal series
نویسندگان
چکیده
منابع مشابه
the investigation of the relationship between type a and type b personalities and quality of translation
چکیده ندارد.
Series Representations for Best Approximating Entire Functions of Exponential Type
Let > 0 not be an even integer. We derive Lagrange type series representations for the entire function of exponential type 1 that minimizes jjjxj f (x)jjLp(R) amongst all such entire functions f , when p = 1 and p =1. This minimum arises as the scaled limit of the Lp error of polynomial approximation of jxj on [ 1; 1], and is one representation of the Lp Bernstein constant.
متن کاملEntire Functions of Exponential Type
it is immaterial which value of z is used in (2). If (1) holds in a region of the s-plane, for example in an angle, ƒ(z) is said to be of exponential type c in that region. Functions of exponential type have been extensively studied, both for their own sake and for their applications. I shall discuss here a selection of their properties, chosen to illustrate how the restriction (1) on the growt...
متن کاملEntire Functions of Exponential Type *
Since this series is absolutely convergent everywhere in the plane, lanl must approach zero as n approaches infinity. Consequently, there exists for each a, an index n(a) for which lanl is a maximal coefficient. B. Lepson [3]1 raised the question of characterizing entire functions for whidi n (a) is bounded in a. 2 In the sequel we shall consider certain interesting variations of Lepson's probl...
متن کاملQuadrature Formulae and Functions of Exponential Type
In this paper we obtain certain generalizations of the trapezoidal rule and the Euler-Maclaurin formula that involve derivatives. In the case of quadrature of functions of exponential type over infinite intervals we find conditions under which existence of the (improper) integral and convergence of the approximating series become equivalent. In the process, we also establish a best possible ver...
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: 2014
ISSN: 0021-9045
DOI: 10.1016/j.jat.2014.02.003