 95337 Brenner A.
 MULTIPARAMETER PSEUDODIFFERENTIAL OPERATORS AND RELATED
SPECTRAL ASYMPTOTICS
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Jun 28, 95

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Abstract. We introduce the notion of ellipticity with parameters and
study elliptic boundary value problems with parameters
in a bounded domain.
Furthermore, the notion of
the ellipticity with parameters for differential and
pseudodifferential operator pencils
is applied to the resolvent construction which leads to the definition
of the corresponding complex powers and $\ \zeta $function,
i.e. to a new functional calculus of operators with
promising applications to the multiparameter spectral theory.
More precisely, we have proved the extension theorem
for traces of the above defined kernels of the complex powers
and the corresponding $\ \zeta $function. The last appears to be
a meromorphic function in $\ C^m\ $ ($m$ is the number of
parameters) with polar sets of the first order
and the corresponding holomorphic residueforms.
In particular, for $m=2$
this investigation gives the opportunity to write the
two  parameter spectral asymptotics in terms of these forms
using the two  dimensional refinement of the Ikehara
Tauberian theorem.
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