Topic
Multiplication operator
About: Multiplication operator is a research topic. Over the lifetime, 3035 publications have been published within this topic receiving 39537 citations.
Papers published on a yearly basis
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Papers
Book•
21 Apr 2003TL;DR: In this article, the reader is provided with a tour of the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, together with some of their main applications.
Abstract: In this book, first published in 2003, the reader is provided with a tour of the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, together with some of their main applications. The author assumes only that the reader has a basic background in functional analysis, and the presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will also want this book for their library since the author illustrates the power of methods he has developed with new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature. An indispensable introduction to the theory of operator spaces for all who want to know more.
2,126 citations
Book•
1 Jan 1993
TL;DR: In this paper, the vertex operator algebras duality for vertex operators and vertex operators for modules is discussed, as well as the duality of vertex operators on modules.
Abstract: Introduction Vertex operator algebras Duality for vertex operator algebras Modules Duality for modules References.
1,304 citations
Book•
27 Jul 1990
TL;DR: A self-contained account of knowledge of the theory of nonlinear superposition operators can be found in this article, where the authors present the main ideas which are useful in studying its properties and provide a comparison of its behaviour in different function spaces.
Abstract: This book is a self-contained account of knowledge of the theory of nonlinear superposition operators: a generalization of the notion of functions. The theory developed here is applicable to operators in a wide variety of function spaces, and it is here that the modern theory diverges from classical nonlinear analysis. The purpose of this book is to collect the basic facts about the superposition operator, to present the main ideas which are useful in studying its properties and to provide a comparison of its behaviour in different function spaces. Some applications are also considered, for example to control theory and optimization. Much of the work here has only appeared before in research literature, which itself is catalogued in detail here.
601 citations
TL;DR: In this article, several definitions of the Riesz fractional Laplace operator in R^d have been studied, including singular integrals, semigroups of operators, Bochner's subordination, and harmonic extensions.
Abstract: This article reviews several definitions of the fractional Laplace operator (-Delta)^{alpha/2} (0 < alpha < 2) in R^d, also known as the Riesz fractional derivative operator, as an operator on Lebesgue spaces L^p, on the space C_0 of continuous functions vanishing at infinity and on the space C_{bu} of bounded uniformly continuous functions. Among these definitions are ones involving singular integrals, semigroups of operators, Bochner's subordination and harmonic extensions. We collect and extend known results in order to prove that all these definitions agree: on each of the function spaces considered, the corresponding operators have common domain and they coincide on that common domain.
568 citations
7 Oct 2004
318 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 7 |
| 2024 | 9 |
| 2023 | 19 |
| 2022 | 38 |
| 2021 | 26 |
| 2020 | 36 |