A “resonance” here is defined to take place iff W (0) = 0 where W (λ) is the Wronskian of the two Jost solutions at energy λ2, see the following section. It is known that the spectrum of H is purely… (More)

In this paper we establish dispersive estimates for solutions to the linear Schrödinger equation in three dimension 1 i ∂tψ −△ψ + V ψ = 0, ψ(s) = f (0.1) where V (t, x) is a time-dependent potential… (More)

We prove the existence of equivariant finite time blow-up solutions for the wave map problem from R2+1 → S2 of the form u(t, r) = Q(λ(t)r)+R(t, r) where u is the polar angle on the sphere, Q(r) = 2… (More)

The distribution of the random series P n is the innnite convolution product of 1 2 (? n + n). These measures have been studied since the 1930's, revealing connections with harmonic analysis, the… (More)

Consider the Schrödinger operator H = −∆ + V in R, where V is a real-valued potential. Let Pac be the orthogonal projection onto the absolutely continuous subspace of L(R) which is determined by H.… (More)

In this paper we consider various regularity results for discrete quasiperiodic Schrödinger equations −ψn+1 − ψn−1 + V (θ + nω)ψn = Eψn with analytic potential V . We prove that on intervals of… (More)

By this we mean that φ > 0 and φ ∈ C2(R3). It is a classical fact (see Coffman [Cof]) that such solutions exist and are unique for the cubic nonlinearity. Moreover, they are radial and smooth.… (More)