| 書目名稱 | Fractal Zeta Functions and Fractal Drums |
| 副標題 | Higher-Dimensional T |
| 編輯 | Michel L. Lapidus,Goran Radunovi?,Darko ?ubrini? |
| 視頻video | http://file.papertrans.cn/348/347339/347339.mp4 |
| 概述 | beginning at the advanced graduate level.The exposition is gentle with numerous instructive examples and illustrations.The book builds on the one-dimensional theory of complex dimensions (the case of |
| 叢書名稱 | Springer Monographs in Mathematics |
| 圖書封面 |  |
| 描述 | This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed step-by-step at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the first time that essential singularities of fractal zeta functions can naturally emerge for various classes of fractal sets and have a significant geometric effect. The theory de |
| 出版日期 | Book 2017 |
| 關鍵詞 | Minkowski measureable; distance zeta function; fractal drum; fractal set; fractal zeta function; tube zet |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-44706-3 |
| isbn_softcover | 978-3-319-83115-2 |
| isbn_ebook | 978-3-319-44706-3Series ISSN 1439-7382 Series E-ISSN 2196-9922 |
| issn_series | 1439-7382 |
| copyright | Springer International Publishing Switzerland 2017 |
|Archiver|手機版|小黑屋|
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