How Long to Read Fractal Zeta Functions and Fractal Drums

How Long Does it Take to Read Fractal Zeta Functions and Fractal Drums?

It takes the average reader 11 hours and 8 minutes to read Fractal Zeta Functions and Fractal Drums by Michel L. Lapidus

Assuming a reading speed of 250 words per minute. Learn more

Description

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.

How long is Fractal Zeta Functions and Fractal Drums?

Fractal Zeta Functions and Fractal Drums by Michel L. Lapidus is 655 pages long, and a total of 167,025 words.

This makes it 221% the length of the average book. It also has 204% more words than the average book.

How Long Does it Take to Read Fractal Zeta Functions and Fractal Drums Aloud?

The average oral reading speed is 183 words per minute. This means it takes 15 hours and 12 minutes to read Fractal Zeta Functions and Fractal Drums aloud.

What Reading Level is Fractal Zeta Functions and Fractal Drums?

Fractal Zeta Functions and Fractal Drums is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Fractal Zeta Functions and Fractal Drums?

Fractal Zeta Functions and Fractal Drums by Michel L. Lapidus is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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