On Taylor coefficients of entire functions integrable against exponential weights (Q2718014)

Given \(p\in N\), the authors deal with the Banachspace \(B_1(p)\) of entire functions belonging to \(L_1(d\mu)\), where \(d\mu(z)=\frac{p}{2n} e^{-|z|^p}|z|^{p-2}d\partial(z)\) and \(d\partial\) stands for the Lebesgue measure on the plane, as well as with the Banach space \(H(e^{-|z|^p})(C)\) of those entire functions \(f\) such that \(\sup_{z\in C}e^{-|z|^p}|f(z)|< \infty\). It has been shown that NEWLINE\[NEWLINE(B_1(p))^*=H(e^{-|z|^p})(C),NEWLINE\]NEWLINE With \(X\) denoting either of \(B_1(p)\) and \(H(e^{-|z|^p})^{(C)}\), the authors discuss the following: given a function \(f(z)=\sum^\infty_{n=0}a_nz_n\) what can be said on the Taylor coefficients \((a_n)\).