An equivalence relation in planar least squares inverse approximation

It is shown that the Planar Least Square Inverse (PLSI) of degree (sm, tn) relative to the lacunary polynomial b(z
1
^s
, z<
2
^t
)is obtained from the PLSI of degree (m, n) relative to b(z
1
, z
2
) by the substitution z
1
→ z
1
^s
, z
2
→ z<
2
^t
.