FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2002, VOLUME 8, NUMBER 1, PAGES 1-16
A. G. Baskakov
Abstract
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We obtain some theorems on splitting of differential operators of the form
$$
\mathcal L = \frac{d}{dt} - A_0 - B A_0^\nu \colon\,
D(\mathcal L) \subset C(\mathbb R,\mathcal Y) \to C(\mathbb R,\mathcal Y)
$$
acting in the Banach space $C(\mathbb R,\mathcal Y)$
of continuous and bounded functions
defined on real axis $\mathbb R$ with values in
the Banach space $\mathcal Y$ .
The linear operator $A_0 \colon\,
D(A_0) \subset \mathcal Y \to \mathcal Y$
is the generating operator
of a strongly continuous semigroup of operators and its spectrum does not
intersect the imaginary axis $i\mathbb R$ .
Here $A_0^\nu$ , $\nu\in [0,1)$ , is a fractional
power of $A_0$ and
$B \colon\, C(\mathbb R,\mathcal Y)
\to C(\mathbb R,\mathcal Y)$ is a bounded
linear operator.
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Last modified: July 8, 2002