Restricted diffusion is a common feature of many physicochemical, biological, and industrial
processes. Nuclear magnetic resonance techniques are often used to survey the atomic or …

This book covers analysis on fractals, a developing area of mathematics which focuses on
the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a …

We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in
bounded Euclidean domains with Dirichlet, Neumann, or Robin boundary condition. We …

This is a comprehensive review of the nodal domains and lines of quantum billiards,
emphasizing a quantitative comparison of theoretical findings to experiments. The nodal …

n This book deals with several aspects of fractal geometry in? which are closely connected
with Fourier analysis, function spaces, and appropriate (pseudo) differ-tial operators. It …

Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with
smooth boundary, are not only of considerable intrinsic interest but have for many years …

This book deals with the constructive Weierstrassian approach to the theory of function
spaces and various applications. The first chapter is devoted to a detailed study of …

We establish an analogue of Weyl's classical theorem for the asymptotics of eigenvalues of
Laplacians on a finitely ramified (ie, pcf) self-similar fractal K, such as, for example, the …

This paper, somewhat delayed in the series “Fundamental Directions,” is devoted to general
linear elliptic boundary problems on a smooth compact manifold with boundary. The paper …

Based on his earlier work on the vibrations of 'drums with fractal boundary', the first author
has refined MV Berry's conjecture that extended from the 'smooth'to the 'fractal'case H …