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Fractal Zeta Functions and Fractal Drums: Higher-Dimensional by Michel L. Lapidus,Goran Radunović,Darko Žubrinić

By Michel L. Lapidus,Goran Radunović,Darko Žubrinić

This monograph offers a state of the art and obtainable remedy of a brand new common higher-dimensional conception of complicated dimensions, legitimate for arbitrary bounded subsets of Euclidean areas, in addition to for his or her typical generalization, relative fractal drums. It offers an important extension of the prevailing thought of zeta features for fractal strings to fractal units and arbitrary bounded units in Euclidean areas of any measurement. new periods of fractal zeta capabilities are brought, particularly, the space and tube zeta capabilities of bounded units, and their key homes are investigated. the idea is constructed step by step at a sluggish speed, and each step is definitely prompted by means of a variety of examples, historic comments and reviews, bearing on the gadgets lower than research to different techniques. detailed emphasis is put on the research of complicated dimensions of bounded units and their connections with the notions of Minkowski content material and Minkowski measurability, in addition to on fractal tube formulation. it's proven for the 1st time that crucial singularities of fractal zeta capabilities can obviously emerge for numerous periods of fractal units and feature an important geometric impression. the idea built during this booklet leads obviously to a brand new definition of fractality, expressed when it comes to the life of underlying geometric oscillations or, equivalently, by way of the life of nonreal complicated dimensions.  
The connections to earlier broad paintings of the 1st writer and his collaborators on geometric zeta features of fractal strings are basically defined. Many innovations are mentioned for the 1st time, making the publication a wealthy resource of recent techniques and ideas to be constructed extra. The ebook encompasses a huge variety of open difficulties and describes many attainable instructions for extra study. the start chapters can be used as part of a path on fractal geometry. the first readership is aimed toward graduate scholars and researchers operating in Fractal Geometry and different similar fields, resembling advanced research, Dynamical structures, Geometric degree thought, Harmonic research, Mathematical Physics, Analytic quantity idea and the Spectral thought of Elliptic Differential Operators. The publication can be available to nonexperts and novices to the field.

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Fractal Zeta Functions and Fractal Drums: Higher-Dimensional Theory of Complex Dimensions (Springer Monographs in Mathematics)

This monograph offers a cutting-edge and available therapy of a brand new basic higher-dimensional conception of advanced dimensions, legitimate for arbitrary bounded subsets of Euclidean areas, in addition to for his or her ordinary generalization, relative fractal drums. It offers an important extension of the prevailing thought of zeta capabilities for fractal strings to fractal units and arbitrary bounded units in Euclidean areas of any measurement.

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