Abstract. The stories told in this paper are dealing with the solution of finite, infinite, and biinfinite Toeplitz-type systems. A crucial role plays the off-diagonal decay behavior of Toeplitz matrices and their inverses. Classical results of Gelfand et al. on commutative Banach algebras yield a general characterization of this decay behavior. We then derive estimates for the approximate solu...

Abstract. Under appropriate assumptions the energy of wave equations with damping and variable coefficients c(x)utt − div(b(x)∇u) + a(x)ut = h(x, t) has been shown to decay. Determining the decay rate for the higher order energies of the kth order spatial and time derivatives has been an open problem with the exception of some sparse results obtained for k = 1, 2. We establish the sharp gain in...

Sufficiently inclusive observables in the decay of the tau lepton can be calculated using the methods of perturbative QCD. These include the asymmetry parameter Aτ that determines that angular distribution of the total hadron momentum in the decay of a polarized tau. It should be possible to measure Aτ accurately using existing data from LEP. Reliable estimates of theoretical errors are essenti...

We show that the nonlinear fourth order degenerate parabolic equation u t + div (u n ru) = 0; n > 0 admits nonnegative solutions to initial data which are a nonnegative Radon measure provided that n < 2. In addition, we prove that the equation has a regularizing eeect in the sense that the solution we construct is in H 1 (R N) for all positive times and in H 2 loc (R N) for almost all positive ...

A general simulation procedure is described to validate model fitting algorithms for complex likelihood functions that are utilized in periodic cancer screening trials. Although screening programs have existed for a few decades, there are still many unsolved problems, such as how age or hormone affects the screening sensitivity, the sojourn time in the preclinical state, and the transition prob...

Anti-viral drug treatment of human immunodeficiency virus type I (HIV-1) and hepatitis B virus (HBV) infections causes rapid reduction in plasma virus load. Viral decline occurs in several phases and provides information on important kinetic constants of virus replication in vivo and pharmacodynamical properties. We develop a mathematical model that takes into account the intracellular phase of...

The purpose of this paper is to show a general Strichartz estimate for certain perturbed wave equation under known local energy decay estimates, and as application, to get the Strauss conjecture for several convex obstacles in n = 3, 4. Our results improve on earlier work in Hidano, Metcalfe, Smith, Sogge and Zhou [14]. First, and most important, we can drop the nontrapping hypothesis and handl...

This work derives sharp estimates for approximation numbers of positive integral operators on the sphere when the generating kernel satisfies an abstract Hölder condition defined by spherical convolutions with uniformly bounded bi-zonal kernels. The estimates are obtained via finite rank operators defined by both, certain generalized Jackson kernels and the operators appearing in the Hölder con...

The semilinear wave equation on the (outer) Schwarzschild manifold is studied. We prove local decay estimates for general (non-radial) data, deriving a-priori Morawetz type inequalities.

We obtain certain time decay and regularity estimates for 3D Schrödinger equation with a potential in the Kato class by using Besov spaces associated with Schrödinger operators.