This book provides a very readable description of a technique,
developed by the author years ago but as current as ever, for
proving that solutions to certain (non-elliptic) partial
differential equations only have real analytic solutions when the
data are real analytic (locally). The technique is completely
elementary but relies on a construction, a kind of a
non-commutative power series, to localize the analysis of high
powers of derivatives in the so-called bad direction. It is hoped
that this work will permit a far greater audience of researchers to
come to a deep understanding of this technique and its power and
flexibility.
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