The subspace Hamiltonian technique, introduced several years ago, has proved convenient for determining bound states and resonances associated with surfaces and defects. Here we discuss the extension of this technique to other problems, including total-energy calculations and real-time computer simulations. %e prove several theorems and report numerical calculations that help to explain the use...

Many problems in mathematics and science require the use of infinite-dimensional spaces. Consequently, there is need for an analogue of the finite-dimensional notions of ‘Lebesgue almost every’ and ‘Lebesgue measure zero’ in the infinite-dimensional setting. The theory of prevalence addresses this need and provides a powerful framework for describing generic behavior in a probabilistic way. We ...