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

By Michel L. Lapidus,Goran Radunović,Darko Žubrinić

ISBN-10: 3319447041

ISBN-13: 9783319447049

This monograph supplies a state of the art and obtainable remedy of a brand new common higher-dimensional thought of complicated dimensions, legitimate for arbitrary bounded subsets of Euclidean areas, in addition to for his or her usual 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, specifically, the space and tube zeta capabilities of bounded units, and their key homes are investigated. the idea is constructed step by step at a gradual speed, and each step is definitely encouraged via a number of examples, historic feedback and reviews, pertaining to the gadgets lower than research to different thoughts. specific emphasis is put on the learn of advanced 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 truly is proven for the 1st time that crucial singularities of fractal zeta capabilities can clearly emerge for varied periods of fractal units and feature an important geometric impact. the speculation built during this e-book leads evidently to a brand new definition of fractality, expressed when it comes to the life of underlying geometric oscillations or, equivalently, when it comes to the life of nonreal advanced dimensions.  
The connections to prior large paintings of the 1st writer and his collaborators on geometric zeta features of fractal strings are basically defined. Many options are mentioned for the 1st time, making the e-book a wealthy resource of recent recommendations and concepts to be built additional. The e-book incorporates a huge variety of open difficulties and describes many attainable instructions for additional learn. the start chapters can be utilized as part of a direction on fractal geometry. the first readership is geared toward graduate scholars and researchers operating in Fractal Geometry and different similar fields, reminiscent of complicated research, Dynamical platforms, Geometric degree concept, Harmonic research, Mathematical Physics, Analytic quantity thought and the Spectral idea of Elliptic Differential Operators. The ebook will be available to nonexperts and rookies to the field.

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Fractal Zeta Functions and Fractal Drums: Higher-Dimensional Theory of Complex Dimensions (Springer Monographs in Mathematics) by Michel L. Lapidus,Goran Radunović,Darko Žubrinić


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