  We study the relationship between integral and infinite-derivative operators.
In particular, we examine the operator $p^{\frac12\,\partial_t^2}\,$ that
appears in the theory of $p$-adic string fields, as well as the Moyal product
that arises in non-commutative theories. We also attempt to clarify the
apparent paradox presented by Moeller and Zwiebach, which highlights the
discrepancy between them.
