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Analytic function

About: Analytic function is a research topic. Over the lifetime, 11598 publications have been published within this topic receiving 183944 citations.


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Book
19 Nov 2010
TL;DR: In this article, the Corona construction was used to construct Douglas algebra and interpolating sequences and Maximal Ideals were used to solve a set of problems in the Corona Construction.
Abstract: Preliminaries.- Hp Spaces.- Conjugate Functions.- Some Extremal Problems.- Some Uniform Algebra.- Bounded Mean Oscillation.- Interpolating Sequences.- The Corona Construction.- Douglas Algebras.- Interpolating Sequences and Maximal Ideals.

3,585 citations

Journal ArticleDOI
TL;DR: In this paper, the Hartree-Fock wave function was used to compute X-ray scattering factors for neutral atoms from He to Lw and for most of the chemically significant ions through Lu3+ through Lu 3+.
Abstract: X-ray scattering factors for neutral atoms from He to Lw and for most of the chemically significant ions through Lu3+ have been computed from numerical Hartree–Fock wave functions. The results are given in the form of coefficients for an analytic function.

2,795 citations

Book
01 Oct 1973
TL;DR: In this article, the authors present an analysis of analytical functions of one complex variable and several complex variables in Commutative Banach Algebras with Stein Manifolds.
Abstract: I. Analytic Functions of One Complex Variable. II. Elementary Properties of Functions of Several Complex Variables. III. Applications to Commutative Banach Algebras. IV. L2 Estimates and Existence Theorems for the Operator. V. Stein Manifolds. VI. Local Properties of Analytic Functions. VII. Coherent Analytic Sheaves on Stein Manifolds. Bibliography. Index.

2,648 citations

Journal ArticleDOI
TL;DR: In this article, a method is developed for treating Einstein's field equations, applied to static spheres of fluid, in such a manner as to provide explicit solutions in terms of known analytic functions.
Abstract: A method is developed for treating Einstein's field equations, applied to static spheres of fluid, in such a manner as to provide explicit solutions in terms of known analytic functions. A number of new solutions are thus obtained, and the properties of three of the new solutions are examined in detail. It is hoped that the investigation may be of some help in connection with studies of stellar structure. (See the accompanying article by Professor Oppenheimer and Mr. Volkoff.)

2,264 citations

Book
01 Jan 1965
TL;DR: The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century after initial successes by Poincare and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable as discussed by the authors.
Abstract: The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century After initial successes by Poincare and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable Beginning in the 1930s, initially through the work of Oka, then H Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resolved many of the open problems and fundamentally changed the landscape of the subject These tools included a central role for sheaf theory and increased uses of topology and algebra The book by Gunning and Rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods The intention of Gunning and Rossi's book is to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces Fundamental concepts and techniques are discussed as early as possible The first chapter covers material suitable for a one-semester graduate course, presenting many of the central problems and techniques, often in special cases The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of analytic spaces

1,469 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023117
2022243
2021417
2020454
2019434
2018386