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Weighted pseudo almost automorphic functions and applications to abstract differential equations. (English) Zbl 1177.34077

The authors investigate many interesting properties of weighted pseudo almost automorphic functions which generalize the well known concept of weighted almost periodic functions. The authors prove a composition theorem for weighted pseudo almost automorphic functions and apply it to show the existence and uniqueness of weighted pseudo almost automorphic mild solutions for some evolution equations whose linear parts generate en exponentially stable semigroups.

MSC:

34G20 Nonlinear differential equations in abstract spaces
44A35 Convolution as an integral transform
42A85 Convolution, factorization for one variable harmonic analysis
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