Functions of Exponential Type
نویسندگان
چکیده
منابع مشابه
Entire 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 کاملInequalities for Entire Functions of Exponential Type
This paper is concerned with a class of linear operators acting in the space of the trigonometric polynomials and preserving the inequalities of the form \S(8)\ < \T(8)\ in the half plane Im 8 > 0. Some inequalities for entire functions of exponential type and some theorems concerning the distribution of the zeros of the trigonometric polynomials, including an analogue to the Gauss-Lucas theore...
متن کاملA Note on Functions of Exponential Type
for all sufficiently large \z\. The following three theorems were proved respectively by D. V. Widder [4], I. J. Schoenberg [2], and H. Poritsky [l] and J. M. Whittaker [3]. THEOREM 1. (Widder.) If a real f unction f (z), of class C ° ° w 0 ^ x ^ l , satisfies the condition (2) ( l)*/ (*) è O , 0 ^ x S 1; n = 0, 1, 2, • • • , then f (x) coincides on (0, 1) with an entire function of exponential...
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...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1969
ISSN: 0002-9947
DOI: 10.2307/1995018