FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 1, PAGES 1-16

Splitting of perturbated differential operators with unbounded operator coefficients

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 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 iR. Here A0n, n Î [0,1), is a fractional power of A0 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