  (Lecture at the workshop "Basic Problems in String Theory", Yukawa Institute
for Theoretical Physics, Kyoto, October 19-21) In this talk, we first review
the possibility of matrix models toward a nonperturbative (critical) string
theory. We then discuss whether the $c=1$ matrix model can describe the black
hole solution of 2D critical string theory. We show that there exists a class
of integral transformations which send the Virasoro condition for the tachyon
field around the 2D black hole to that around the linear dilaton vacuum. In
particular, we construct an explicit integral formula wihich describes a
continuous deformation of the linear dilaton vacuum to the black hole
background.
