Abstract
Let σ(x) be a nondecreasing function, such that σ(-∞) = 0,σ(-∞) = 1 a nd let us denote by B the class of functions which can be represented by a Fourier–Stieltjes integral \(f(t)=\int^\infty_{-\infty}\;e^{itx}d\sigma(x)\). The purpose of this chapter is to give a characterization of the class B and to give a generalization of the classical theorem of Bochner in the framework of quaternion analysis.
Mathematics Subject Classification (2010). Primary 30G35; secondary 42A38.
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References
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Georgiev, S., Morais, J. (2013). Bochner’s Theorems in the Framework of Quaternion Analysis. In: Hitzer, E., Sangwine, S. (eds) Quaternion and Clifford Fourier Transforms and Wavelets. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0603-9_5
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DOI: https://doi.org/10.1007/978-3-0348-0603-9_5
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