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Abstract In this paper, by using operator-valued ${\dot{C}}^{\unicode[STIX]{x1D6FC}}$ -Fourier multiplier results on vector-valued Hölder continuous function spaces, we give a characterization of the $C^{\unicode[STIX]{x1D6FC}}$ -well-posedness for the third order differential… Click to show full abstract
Abstract In this paper, by using operator-valued ${\dot{C}}^{\unicode[STIX]{x1D6FC}}$ -Fourier multiplier results on vector-valued Hölder continuous function spaces, we give a characterization of the $C^{\unicode[STIX]{x1D6FC}}$ -well-posedness for the third order differential equations $au^{\prime \prime \prime }(t)+u^{\prime \prime }(t)=Au(t)+Bu^{\prime }(t)+f(t)$ , ( $t\in \mathbb{R}$ ), where $A,B$ are closed linear operators on a Banach space $X$ such that $D(A)\subset D(B)$ , $a\in \mathbb{C}$ and $0<\unicode[STIX]{x1D6FC}<1$ .
Journal Title: Canadian Mathematical Bulletin
Year Published: 2019
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