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.

Australia Telescope Compact Array 1.2cm Observations of the Massive Star Forming Region G305.2+0.2

We report on Australia Telescope Compact Array observations of the massive star-forming region G305.2+0.2 at 1.2 cm. We detected emission in five molecules towards G305A, confirming its hot core nature. We determined a rotational temperature of 26 K for methanol. A non-local thermodynamic equilibrium excitation calculation suggests a kinematic temperature of the order of 200 K. A time-dependent chemical model is also used to model the gas-phase chemistry of the hot core associated with G305A. A comparison with the observations suggest an age of between 2 × 104 and 1.5 × 105 yr. We also report on a feature to the south-east of G305A which may show weak Class I methanol maser emission in the line at 24.933 GHz. The more evolved source G305B does not show emission in any of the line tracers, but strong Class I methanol maser emission at 24.933 GHz is found 3 arcsec to the east. Radio continuum emission at 18.496 GHz is detected towards two H ii regions. The implications of the non-detection of radio continuum emission towards G305A and G305B are also discussed.