**
Below is the ascii version of the abstract for 03-551.
The html version should be ready soon.**Masao Hirokawa
Mathematical Addendum for ``Infrared Catastrophe for Nelson's Model" (mp_arc 03-512)
(195K, Postscript)
ABSTRACT. In [mp_arc 03-512], the author used the kernel $a(k)$ of annihilation operator of bosons to describe and prove several useful formulas such as
the pull-through formula on ground states. So, it is somewhat formal
in the light of mathematics. Indeed, it is no wonder some mathematicians
think the arguments by the symbolical formulas with $a(k)$ are so formal
that they are incredulous of the arguments because of the well-known
difficulty on the domain of $a(k)$. Thus, in this addendum, we list
the difficulty in Remark 1 first. In order to treat it, we restate
the formulas by using the smeared annihilation operator $a(f)$,
$f \in L^{2}({\bf R}^{3})$, instead of $a(k)$ and present mathematically
rigorous proofs of them. To author's best knowledge, the ways to prove
them have not appeared in literatures yet. In this addendum, we use
the same notations as in [mp_arc 03-512].