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Abstract
In , we consider a selfadjoint operator
,
, given by the differential expression
, where
is the first-order differential operator, and
are matrix-valued functions in
periodic with respect to some lattice
. It is assumed that g is bounded and positive definite, while
and Q are, in general, unbounded. We study the generalized resolvent
, where
is a
-periodic, bounded and positive definite matrix-valued function, and
is a complex-valued parameter. Approximations for the generalized resolvent in the
- and
-norms with two-parametric error estimates (with respect to the parameters
and
) are obtained.
AMS Subject Classifications:
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
Supported by RFBR [project number 14-01-00760]; SPbSU [project number 11.38.263.2014]. The first author is supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government grant 11.G34.31.0026 and by JSC “Gazprom Neft”.