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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Arithmetik & Algebra Fractal Zeta Functions and Fractal Drums
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Fractal Zeta Functions and Fractal Drums
Michel L. Lapidus, Goran Radunović, Darko Žubrinić (Gebundene Ausgabe, Englisch)
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Beschreibung
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 developed in this book leads naturally to a new definition of fractality, expressed in terms of the existence of underlying geometric oscillations or, equivalently, in terms of the existence of nonreal complex dimensions. The connections to previous extensive work of the first author and his collaborators on geometric zeta functions of fractal strings are clearly explained. Many concepts are discussed for the first time, making the book a rich source of new thoughts and ideas to be developed further. The book contains a large number of open problems and describes many possible directions for further research. The beginning chapters may be used as a part of a course on fractal geometry. The primary readership is aimed at graduate students and researchers working in Fractal Geometry and other related fields, such as Complex Analysis, Dynamical Systems, Geometric Measure Theory, Harmonic Analysis, Mathematical Physics, Analytic Number Theory and the Spectral Theory of Elliptic Differential Operators. The book should be accessible to nonexperts and newcomers to the field. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
26.06.2017
Sprache
Englisch
EAN
9783319447049
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Springer Monographs in Mathematics
Sonderedition
Nein
Autor
Michel L. Lapidus, Goran Radunović, Darko Žubrinić
Seitenanzahl
655
Einbandart
Gebundene Ausgabe
Buch Untertitel
Higher-Dimensional Theory of Complex Dimensions
Schlagwörter
Minkowski measureable, distance zeta function, fractal drum, fractal set, fractal zeta function, tube zeta function, zeta function, geometric zeta function, fractal string, relative fractal drum, Minkowski content, Dirichlet series, cone property, exponent sequence, Cantor set
Thema-Inhalt
PBH - Zahlentheorie
PBKL - Integralrechnung und -gleichungen
PHU - Mathematische Physik
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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