**Authors**:
G.Benfatto, M.Cassandro, G.Gallavotti, F.Nicol\`o, E.Olivieri,
E.Presutti, E.Scacciatelli

**Title**:
*
Ultraviolet Stability in Euclidean Scalar Field Theories
*

Communication in Mathematical Physics, ** 71**, 95--130, 1980

**Abstract:** We develop a technique for reducing
the problem of the ultraviolet divergences and their removal to a free
field problem. This work is an example of a problem to which a rather
general method can be applied. It can be thought as an attempt towards
a rigorous version (in 2 or 3 space-time dimensions) of the analysis
of the structure of the functional integrals developed in [9], the
underlying mechanism being essentially the same as in [11,3].

**Key words: **
Quantum fields, Constructive field theory, Hierarchical models,
Ultraviolet stability, Asymptotic freedom, Perturbation theory