there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.

Abstract. We compute the production of particles from the gravitational field of an expanding mass shell. Contrary to the situation of Hawking radiation and the production of cosmological perturbations during cosmological inflation, the example of an expanding mass shell has no horizon and no singularity. We apply the method of ‘ray-tracing’, first introduced by Hawking, and calculate the energ...

We develop a new method to determine the linear mass power spectrum using the mass function of galaxy clusters. We obtain the rms mass fluctuation σ(M) using the expression for the mass function in the Press & Schechter (1974), Sheth, Mo & Tormen (2001) & Jenkins et al. (2001) formalisms. We apply different techniques to recover the adimensional power spectrum ∆(k) from σ(M) namely the keff app...

We analyze the flux power spectrum and its covariance using simulated Lyα forests. We find that pseudo-hydro techniques are good approximations of hydrodynamical simulations at high redshift. However, the pseudo-hydro techniques fail at low redshift because they are insufficient for characterizing some components of the low-redshift intergalactic medium, notably the warm-hot intergalactic mediu...