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 $\mathbb R$ 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