Polynomials on Banach spaces with unconditional bases

We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of the domain.

Bright Multi-keV Harmonic Generation from Relativistically Oscillating Plasma Surfaces

The first evidence of x-ray harmonic radiation extending to 3.3 A, 3.8 keV (order n > 3200) from petawatt class laser-solid interactions is presented, exhibiting relativistic limit efficiency scaling (eta similar to n(-2.5)-n(-3)) at multi-keV energies. This scaling holds up to a maximum order, n(RO)similar to 8(1/2)gamma(3), where gamma is the relativistic Lorentz factor, above which the first evidence of an intensity dependent efficiency rollover is observed. The coherent nature of the generated harmonics is demonstrated by the highly directional beamed emission, which for photon energy h nu > 1 keV is found to be into a cone angle similar to 4 degrees, significantly less than that of the incident laser cone (20 degrees).