A partial converse to the Riemann--Lebesgue lemma for Bessel--Fourier series of order zero

Ryan L. Acosta Babb

It is known that the Bessel--Fourier coefficients $f_m$ of a function $f$ such that $\sqrt{x}f(x)$ is integrable over $[0,1]$ satisfy $f_m/\sqrt{m}\to 0$. We show a partial convers…