Topic
Automorphic function
About: Automorphic function is a research topic. Over the lifetime, 122 publications have been published within this topic receiving 3245 citations.
Papers published on a yearly basis
Papers
31 Dec 1964
TL;DR: The main purpose of as mentioned in this paper is to bring together in one place both the classical and modern aspects of the theory, and to present them clearly and in a modern language and notation.
Abstract: Much has been written on the theory of discontinuous groups and automorphic functions since 1880, when the subject received its first formulation. The purpose of this book is to bring together in one place both the classical and modern aspects of the theory, and to present them clearly and in a modern language and notation. The emphasis in this book is on the fundamental parts of the subject. The book is directed to three classes of readers: graduate students approaching the subject for the first time, mature mathematicians who wish to gain some knowledge and understanding of automorphic function theory, and experts.
513 citations
1 Jan 2001
TL;DR: In this paper, almost automorphic functions with values in a Banach space and almost periodic solutions of the Equation x' = Ax + f in Locally Convex Spaces.
Abstract: 1. Introduction and Preliminaries. 2. Almost Automorphic Functions with Values in a Banach Space. 3. Almost Periodic Functions with Values in a Linear Topological Space. 4. The Equation x'(t) = Ax(t) + f(t).5. The Equation x' = f(t,x). 6. A Case of One-to-One Correspondence between Almost Automorphic and Asymptotically Almost Automorphic Solutions. 7. Almost Periodic Solutions of the Equation x' = Ax + f in Locally Convex Spaces. 8. Almost Periodic Solutions of Differential Equations in Normed Spaces. References. Index.
467 citations
290 citations
Book•
1 Jan 2005
TL;DR: In this article, almost automorphic evolution functions have been used for abstract dynamical systems, where the inhomogeneous equation x' = Ax + f 2 2.1.
Abstract: 1: Introduction and Preliminaries 1.1 Measurable Functions 1.2 Sobolev Spaces 1.3 Semigroups of Linear Operators 1.4 Fractional Powers of Operators 1.5 Evolution Equations 1.6 Almost Automorphic Functions 1.6.1 Asymptotically Almost Automorphic Functions 1.6.2 Applications to Abstract Dynamical Systems 1.7 Almost Periodic Functions 1.8 Bibliographical Remarks and Open Problems 2: Almost Automorphic Evolution Equations 2.1 Linear Equations 2.1.1 The inhomogeneous equation x' = Ax + f 2.1.2 Method of Invariant Subspaces 2.1.3 Almost Automorphic Solutions to Some Second-Order Hyperbolic Equations 2.2 Nonlinear Equations 2.2.1 Existence of Almost Automorphic Mild Solutions-Case I 2.2.2 Existence of Almost Automorphic Mild Solutions-Case II 2.3 Optimal weak-almost periodic solutions 2.4 Existence of Weakly Almost Automorphic Solutions 2.5 A Correspondence Between Linear and Nonlinear Equations 3: Almost Periodicity in Fuzzy Setting 3.1 Fuzzy Sets 3.2 Almost Periodicity in Fuzzy Setting 3.3 Harmonics of Almost Periodic Functions in Fuzzy Setting 3.4 Applications to Fuzzy Differential Equations 3.5 Bibliographical Remarks and Open Problems 4: Almost Automorphy in Fuzzy Setting 4.1 Introduction 4.2 Preliminaries 4.3 Basic Definitions and Properties 4.4 Applications to Fuzzy Differential Equations 4.5 Bibliographical Remarks and Open Problems References Index
275 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 7 |
| 2019 | 4 |
| 2018 | 2 |
| 2017 | 2 |
| 2016 | 4 |