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Fractal Zeta Functions and Fractal Drums : Higher-Dimensional Theory of Complex Dimensions by Michel L. Lapidus, Goran Radunović and Darko Žubrinić is a nonfiction available to read on EtoBox.

What is Fractal Zeta Functions and Fractal Drums : Higher-Dimensional Theory of Complex Dimensions about?

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

Who reads Fractal Zeta Functions and Fractal Drums : Higher-Dimensional Theory of Complex Dimensions?

Author

Michel L. Lapidus, Goran Radunović and Darko Žubrinić

Publisher

Springer International Publishing, Cham

Published

2017

Language

EN

ISBN

9783319447049

Category

nonfiction

Subjects

Mathematics, Science, Physics