Number Theory

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

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By Michel L. Lapidus,Goran Radunović,Darko Žubrinić

ISBN-10: 3319447041

ISBN-13: 9783319447049

This monograph offers a cutting-edge and obtainable therapy of a brand new normal higher-dimensional concept of complicated dimensions, legitimate for arbitrary bounded subsets of Euclidean areas, in addition to for his or her common generalization, relative fractal drums. It presents an important extension of the prevailing concept of zeta services for fractal strings to fractal units and arbitrary bounded units in Euclidean areas of any size. new sessions of fractal zeta services are brought, particularly, the space and tube zeta services of bounded units, and their key homes are investigated. the speculation is constructed step by step at a sluggish speed, and each step is easily stimulated by means of a number of examples, ancient comments and reviews, pertaining to the items below research to different suggestions. specific emphasis is put on the research 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 services can evidently emerge for numerous sessions of fractal units and feature an important geometric impression. the speculation constructed during this ebook leads certainly to a brand new definition of fractality, expressed by way of the life of underlying geometric oscillations or, equivalently, when it comes to the lifestyles of nonreal advanced dimensions.  
The connections to prior vast paintings of the 1st writer and his collaborators on geometric zeta capabilities of fractal strings are essentially defined. Many options are mentioned for the 1st time, making the e-book a wealthy resource of recent suggestions and ideas to be constructed additional. The ebook incorporates a huge variety of open difficulties and describes many attainable instructions for extra learn. the start chapters can be used as part of a path on fractal geometry. the first readership is geared toward graduate scholars and researchers operating in Fractal Geometry and different similar fields, resembling advanced research, Dynamical platforms, Geometric degree concept, Harmonic research, Mathematical Physics, Analytic quantity conception and the Spectral idea of Elliptic Differential Operators. The ebook might be available to nonexperts and beginners 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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