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Maximal regular convolution-differential equations in weighted Besov spaces. (English) Zbl 1474.34401

Summary: By using Fourier multiplier theorems, the maximal regularity properties of abstract convolution differential equations in weighted Besov spaces are investigated. It is shown that the corresponding convolution differential operators are positive and generate analytic semigroups in abstract Besov spaces. Then, the well-posedness of the Cauchy problem for parabolic convolution – operator equation is established. Moreover, these results are used to establish maximal regularity properties for system of integro-differential equations of finite and infinite orders.

MSC:

34G10 Linear differential equations in abstract spaces
34G20 Nonlinear differential equations in abstract spaces
45J05 Integro-ordinary differential equations
30H25 Besov spaces and \(Q_p\)-spaces
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