Finite rank Bargmann–Toeplitz operators with non-compactly supported symbols

Theorems about characterization of finite rank Toeplitz operators inFock–Segal–Bargmann spaces, known previously only for symbolswith compact support,are carried over to symbols without that restriction, however with a rather rapiddecay at infinity. The proof is based upon a new version of the Stone–Weierstrassapproximation theorem