Topic
Quasi-analytic function
About: Quasi-analytic function is a research topic. Over the lifetime, 764 publications have been published within this topic receiving 10994 citations.
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Papers
Book•
1 Jun 1996
TL;DR: In this article, the authors considered the problem of the growth of an entire function and the distribution of its zeros, and they gave a lower bound on the maximum number of zeros of a function in the half-plane.
Abstract: Part I. Entire Functions of Finite Order: Growth of entire functions Main integral formulas for functions analytic in a disk Some applications of the Jensen formula Factorization of entire functions of finite order The connection between the growth of an entire function and the distribution of its zeros Theorems of Phragmen and Lindelof Subharmonic functions The indicator function The Polya Theorem Applications of the Polya Theorem Lower bounds for analytic and subharmonic functions Entire functions with zeros on a ray Entire functions with zeros on a ray (continuation) Part II. Entire Functions of Exponential Type: Integral representation of functions analytic in the half-plane The Hayman Theorem Functions of class $C$ and their applications Zeros of functions of class $C$ Completeness and minimality of system of exponential functions in $L^2(0,a)$ Interpolation by entire functions of exponential type Interpolation by entire functions of the spaces $L_\pi$ and $B_\pi$ Sin-type functions Riesz bases formed by exponential functions in $L^2(-\pi,\pi)$ Completeness of the eigenfunction system of a quadratic operator pencil Part III. Some Additional Problems of the Theory of Entire Functions: Carleman's and R. Nevanlinna's formulas and their applications Uniqueness problems for Fourier transforms and for infinitely-differentiable functions The Matsaev Theorem on the growth of entire functions admitting a lower bound Entire functions of the class $P$ S. N. Bernstein's inequality for entire functions of exponential type and its generalizations Bibliography Author index Subject index.
1,224 citations
1 Apr 1990
TL;DR: Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g = f − 1 satisfying the conditions that z f / f ( z ) and z g / g ( z) are both subordinate to a univalent function whose range is symmetric with respect to the real axis.
277 citations
TL;DR: An interesting subclass N h ;p Σ ( ; ) of analytic and bi-univalent functions in the open unit disk U is introduced and estimates on the first two Taylor-Maclaurin coefficients are obtained.
273 citations
TL;DR: An algorithm that performs this evaluation for an arbitrary analytic function f(~) is described, and a short FORTRAN program for generating up to 50 leading derivatives is to be found in the algorithm section of this issue.
Abstract: It is well known that the classical difference formulas for evaluating high derivatives of a real function
f(ζ) are very ill-conditioned. However, if the function f(ζ) is analytic and can be evaluated for
complex values of ζ, the problem can be shown to be perfectly well-conditioned. An algorithm that
performs this evaluation for an arbitrary analytic function f(~) is described. A short FORTRAN
program for generating up to 50 leading derivatives is to be found in the algorithm section of this
issue. To use this program, no knowledge is required either of the method or of the analytical nature
(e.g., position of nearest singularity, its type) of the function.
198 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 6 |
| 2023 | 3 |
| 2022 | 5 |
| 2018 | 2 |
| 2017 | 16 |