Werner O. Amrein Knihy

The relevance of commutator methods in spectral and scattering theory has long been recognized, yielding numerous notable results. For further insight, readers can refer to works by Putnam, Reed-Simon, and Baumgartel-Wollenberg. A significant advancement occurred around 1979 with E. Mourre's introduction of locally conjugate operators, which greatly enhanced the understanding of spectral properties in N-body Hamiltonians. This method simplified the previously challenging problem of proving the absence of singularly continuous spectrum for such operators, a feat accomplished by Mourre for N = 3 and later by Perry, Sigal, and Simon for general N. The Mourre estimate, central to this approach, also impacts the long-term behavior of N-body systems. In 1985, Sigal and Soffer further explored these propagation properties, establishing the existence and completeness of wave operators for N-body systems with short-range interactions, without imposing implicit conditions on the potentials. Prior to this, similar results for N = 3 were achieved through time-dependent methods by Enss and Sinha, Krishna, and Muthuramalingam. Our interest in commutator methods stems from these significant advancements.

Covers a unique meeting (200th anniversary of the birth of Charles Sturm) Combines history with current research Internationally renowned authors Tribute to a great Swiss mathematician Includes supplementary material: sn. pub/extras