منابع مشابه
Analytic Functions and Boundary Values
Analytic functions in tubes T B = R+iB in C, where B 1⁄2 R, that generalize the Hardy H spaces are studied. The associated function M¤ of Komatsu, which is de ̄ned with the aid of certain sequences of positive real numbers, is involved in the generalizing bound of the L norm. Fourier-Laplace and Cauchy integral representations are obtained for these functions. These representations can be used t...
متن کاملBoundary Values of Continuous Analytic Functions
Let U, K, and C denote the open unit disc, the closed unit disc, and the unit circumference, respectively. Let A be the set of all complex-valued functions which are defined and continuous on K and analytic in U. The theorem proved in this paper states that if £ is a closed subset of C, of (Lebesgue) measure zero, and if <p is a continuous function defined on £, then there exists a function /£....
متن کاملAnalytic Functions in Smirnov Classes E with Real Boundary Values
Smirnov domains with non-smooth boundaries do admit non-trivial functions of Smirnov class with real boundary values. We will show that the existance of functions in Smirnov classes with real boundary values is directly dependent on the boundary characteristics of a Smirnov domain. Mathematics Subject Classification (2000). 30H10, 30H15.
متن کاملAlgebraic values of analytic functions
Given an analytic function of one complex variable f , we investigate the arithmetic nature of the values of f at algebraic points. A typical question is whether f(α) is a transcendental number for each algebraic number α. Since there exist transcendental entire functions f such that f (t)(α) ∈ Q[α] for any t ≥ 0 and any algebraic number α, one needs to restrict the situation by adding hypothes...
متن کاملOn a boundary property of analytic functions
Let f be an analytic function in the unit disc [Formula: see text] on the complex plane [Formula: see text]. This paper is devoted to obtaining the correspondence between [Formula: see text] and [Formula: see text] at the point w, [Formula: see text], such that [Formula: see text]. We present several applications of the main result. A part of them improve the previous results of this type.
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: Far east journal of applied mathematics
سال: 2023
ISSN: ['0972-0960']
DOI: https://doi.org/10.17654/0972096023011