  We consider a class of linear Volterra transforms of Brownian motion
associated to a sequence of M\"untz Gaussian spaces and determine explicitly
their kernels; some interesting links with M\"untz-Legendre polynomials are
provided. This gives new explicit examples of progressive Gaussian enlargement
of the Brownian filtration. By exploiting a link to stationarity, we give a
necessary and sufficient condition for the existence of kernels of infinite
order associated to an infinite dimensional M\"untz Gaussian space; we also
examine when the transformed Brownian motion remains a semimartingale in the
filtration of the original process.
