Abstract:
We prove that there are no linear algorithms of affine synthesis
for affine systems in the Lebesgue space $L^1[0,1]$ with respect to the
model space $\ell^1$, although the corresponding affine
synthesis problem has a positive solution under the most general
assumptions. At the same time, by imposing additional conditions
on the generating function of the affine system, we can give an explicit
linear algorithm of affine synthesis in the Lebesgue space when the
model space is that of the coefficients of the system.
This linear algorithm generalizes the Fourier–Haar expansion
into orthogonal series.
Fulltext:
PDF file (657 kB)
