| 书目名称 | Monotone Matrix Functions and Analytic Continuation |
| 编辑 | William F. Donoghue |
| 视频video | |
| 丛书名称 | Grundlehren der mathematischen Wissenschaften |
| 图书封面 |  |
| 描述 | A Pick function is a function that is analytic in the upper half-plane with positive imaginary part. In the first part of this book we try to give a readable account of this class of functions as well as one of the standard proofs of the spectral theorem based on properties of this class. In the remainder of the book we treat a closely related topic: Loewner‘s theory of monotone matrix functions and his analytic continuation theorem which guarantees that a real function on an interval of the real axis which is a monotone matrix function of arbitrarily high order is the restriction to that interval of a Pick function. In recent years this theorem has been complemented by the Loewner-FitzGerald theorem, giving necessary and sufficient conditions that the continuation provided by Loewner‘s theorem be univalent. In order that our presentation should be as complete and trans parent as possible, we have adjoined short chapters containing the in formation about reproducing kernels, almost positive matrices and certain classes of conformal mappings needed for our proofs. |
| 出版日期 | Book 1974 |
| 关键词 | Analytische Funktion; Monotone Funktion; function; proof; spectral theorem; theorem |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-642-65755-9 |
| isbn_softcover | 978-3-642-65757-3 |
| isbn_ebook | 978-3-642-65755-9Series ISSN 0072-7830 Series E-ISSN 2196-9701 |
| issn_series | 0072-7830 |
| copyright | Springer-Verlag Berlin Heidelberg 1974 |
发表于 2025-3-21 19:25:44
