Overview
- Authors:
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Le Hai Khoi
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Department of General Education, University of Science and Technology of Hanoi, Vietnam Academy of Science and Technology, Hanoi, Vietnam
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Javad Mashreghi
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Department of Mathematics and Statistics, Université Laval, Québec, Canada
- Presents recent research on Banach and Hilbert spaces of analytic functions on the open unit disc D
- Encourages readers to pursue further study in this area by using generalized definitions
- Offers an overview of current trends in this active area of research
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Other ways to access
Table of contents (12 chapters)
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- Le Hai Khoi, Javad Mashreghi
Pages 1-25
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- Le Hai Khoi, Javad Mashreghi
Pages 27-38
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- Le Hai Khoi, Javad Mashreghi
Pages 39-53
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- Le Hai Khoi, Javad Mashreghi
Pages 55-70
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- Le Hai Khoi, Javad Mashreghi
Pages 71-90
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- Le Hai Khoi, Javad Mashreghi
Pages 91-107
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- Le Hai Khoi, Javad Mashreghi
Pages 109-121
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- Le Hai Khoi, Javad Mashreghi
Pages 123-151
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- Le Hai Khoi, Javad Mashreghi
Pages 153-171
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- Le Hai Khoi, Javad Mashreghi
Pages 173-186
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- Le Hai Khoi, Javad Mashreghi
Pages 187-213
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- Le Hai Khoi, Javad Mashreghi
Pages 215-250
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Back Matter
Pages 251-258
About this book
This monograph provides a comprehensive study of a typical and novel function space, known as the $\mathcal{N}_p$ spaces. These spaces are Banach and Hilbert spaces of analytic functions on the open unit disk and open unit ball, and the authors also explore composition operators and weighted composition operators on these spaces. The book covers a significant portion of the recent research on these spaces, making it an invaluable resource for those delving into this rapidly developing area. The authors introduce various weighted spaces, including the classical Hardy space $H^2$, Bergman space $B^2$, and Dirichlet space $\mathcal{D}$. By offering generalized definitions for these spaces, readers are equipped to explore further classes of Banach spaces such as Bloch spaces $\mathcal{B}^p$ and Bergman-type spaces $A^p$. Additionally, the authors extend their analysis beyond the open unit disk $\mathbb{D}$ and open unit ball $\mathbb{B}$ by presenting families of entire functions in the complex plane $\mathbb{C}$ and in higher dimensions. The Theory of $\mathcal{N}_p$ Spaces is an ideal resource for researchers and PhD students studying spaces of analytic functions and operators within these spaces.
Authors and Affiliations
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Department of General Education, University of Science and Technology of Hanoi, Vietnam Academy of Science and Technology, Hanoi, Vietnam
Le Hai Khoi
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Department of Mathematics and Statistics, Université Laval, Québec, Canada
Javad Mashreghi
About the authors
Javad Mashreghi is an esteemed mathematician and author renowned for his work in the areas of functional analysis, operator theory, and complex analysis. He has made significant contributions to the study of analytic function spaces and the operators that act upon them. Prof. Mashreghi has held various prestigious positions throughout his career. He served as the 35th President of the Canadian Mathematical Society (CMS) and has been recognized as a Lifetime Fellow of both CMS and the Fields Institute. He currently holds the Canada Research Chair at Université Laval and has also been honored as a Fulbright Research Chair at Vanderbilt University.
Le Hai Khoi is an expert in the fields of function spaces and operator theory, with a particular focus on the representation of functions using series expansions involving exponential functions, rational functions, and Dirichlet series. He has made significant contributions to these areas and has a prolific research output, having published over 80 research papers in the relevant field. Prof. Le Hai Khoi is well-known for his expertise and active involvement in the study of $\mathcal{N}_p$ spaces, which are Banach and Hilbert spaces of analytic functions on the open unit disk and open unit ball.
