Memoirs of the American Mathematical Society 1997; 97 pp; softcover Volume: 127 ISBN10: 0821805975 ISBN13: 9780821805978 List Price: US$43 Individual Members: US$25.80 Institutional Members: US$34.40 Order Code: MEMO/127/608
 This memoir provides a detailed study of the effect of non powerlike irregularities of (the geometry of) the fractal boundary on the spectrum of "fractal drums" (and especially of "fractal strings"). In this work, the authors extend previous results in this area by using the notion of generalized Minkowski content which is defined through some suitable "gauge functions" other than power functions. (This content is used to measure the irregularity (or "fractality") of the boundary of an open set in \(R^n\) by evaluating the volume of its small tubular neighborhoods.) In the situation when the power function is not the natural "gauge function", this enables the authors to obtain more precise estimates, with a broader potential range of applications than in previous papers of the second author and his collaborators. Readership Graduate students and research mathematicians interested in dynamical systems, fractal geometry, partial differential equations, analysis, measure theory, number theory or spectral geometry. Physicists interested in fractal geometry, condensed matter physics or wave propagation in random or fractal media. Table of Contents  Introduction
 Statement of the main results
 Sharp error estimates and their converse when \(n=1\)
 Spectra of fractal strings and the Riemann zetafunction
 The complex zeros of the Riemann zetafunction
 Error estimates for \(n\geq 2\)
 Examples
 Appendix: Examples of Gauge functions
 References
