Analysis on Fock Spaces
Analysis on Fock Spaces
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DOI：
10.1007/978-1-4419-8801-0
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发表时间：
2012-05
期刊：
影响因子：
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通讯作者：
Kehe Zhu
中科院分区：
文献类型：
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作者：
Kehe Zhu
在过去的几十年里，解析函数的几种自然Lp空间得到了广泛的研究，包括哈代空间，Bergman空间和Fock空间。术语“哈代空间”和“伯格曼空间”到目前为止是标准的和公认的。但“福克空间”这个术语是另一回事。关于哈代空间的主题，现在有许多优秀的书籍。几本关于伯格曼空间的书，包括作者的一些书，也在过去的几十年里出现。但是市场上还没有关于福克空间的书。本书的目的就是填补这一空白，特别是当这个主题的许多结果到现在已经完成的时候。这本书提出了重要的结果和技术总结在一个地方，使新来者，特别是研究生，有一个方便的参考主题。这本书包含的证据是新的和简单的比现有的文献。特别是，这本书避免使用海森堡群，傅里叶变换，和热方程。这有助于将先决条件保持在最低限度。真实的分析、复分析和泛函分析的每一门标准研究生课程都应该为读者做好充分的准备。
Several natural Lp spaces of analytic functions have been widely studied in the past few decades, including Hardy spaces, Bergman spaces, and Fock spaces. The terms “Hardy spaces” and “Bergman spaces” are by now standard and well established. But the term “Fock spaces” is a different story. Numerous excellent books now exist on the subject of Hardy spaces. Several books about Bergman spaces, including some of the author’s, have also appeared in the past few decades. But there has been no book on the market concerning the Fock spaces. The purpose of this book is to fill that void, especially when many results in the subject are complete by now. This book presents important results and techniques summarized in one place, so that new comers, especially graduate students, have a convenient reference to the subject. This book contains proofs that are new and simpler than the existing ones in the literature. In particular, the book avoids the use of the Heisenberg group, the Fourier transform, and the heat equation. This helps to keep the prerequisites to a minimum. A standard graduate course in each of real analysis, complex analysis, and functional analysis should be sufficient preparation for the reader.