|
Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
|
Buy Now
Fractal Zeta Functions and Fractal Drums - Higher-Dimensional Theory of Complex Dimensions (Hardcover, 1st ed. 2017)
Loot Price: R2,325
Discovery Miles 23 250
You Save: R1,530
(40%)
|
|
|
Fractal Zeta Functions and Fractal Drums - Higher-Dimensional Theory of Complex Dimensions (Hardcover, 1st ed. 2017)
Series: Springer Monographs in Mathematics
Expected to ship within 12 - 19 working days
|
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.
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
|
You might also like..
|
Welcome to Loot.co.za!
Sign in / Register |Wishlists & Gift Vouchers |Help | Advanced search
