The spectral mapping theorem for joint approximate point spectrum is proved when A is an «-tuple of commuting operators on a Banach space and ƒ is any w-tuple of rational functions for which f (A) is defined. The purpose of the paper is to show how properties of parts of the joint spectrum can be obtained by use of spaces of sequences of vectors. The method (first used for general Banach spaces...

This note is a summary of the results of my Ph.D. thesis (plus slight modifications), completed May 9, 2003, under the supervision of Professor Paul Goerss at Northwestern University. Let En be the Lubin-Tate spectrum with En∗ = W (Fpn)[[u1, ..., un−1]][u], where the degree of u is −2 and the complete power series ring over the Witt vectors is in degree zero. Let Gn = Sn o Gal(Fpn/Fp), where Sn...

We study the Floquet Hamiltonian −i∂t + H + V (ωt), acting in L([ 0, T ],H, dt), as depending on the parameter ω = 2π/T . We assume that the spectrum of H in H is discrete, Spec(H) = {hm}m=1, but possibly degenerate, and that t 7→ V (t) ∈ B(H) is a 2π-periodic function with values in the space of Hermitian operators on H. Let J > 0 and set Ω0 = [ 89J, 98J ]. Suppose that for some σ > 0 it holds...

The renormalization group (RG) approach is largely responsible for the considerable success that has been achieved in developing a quantitative theory of phase transitions. Physical properties emerge from spectral properties of the linearization of the RG map at a fixed point. This article considers RG for classical Ising-type lattice systems. The linearization acts on an infinite-dimensional B...

We introduce a class of real analytic “peaky” potentials for which the corresponding quasiperiodic 1D-Schrödinger operators exhibit, frequencies in set positive Lebesgue measure, both absolutely continuous and pure point spectrum.