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Power series as Fourier series. (English) Zbl 1510.32001

Summary: An abstract theory of Fourier series in locally convex topological vector spaces is developed. An analog of Fejér’s theorem is proved for these series. The theory is applied to distributional solutions of Cauchy-Riemann equations to recover basic results of complex analysis. Some classical results of function theory are also shown to be consequences of the series expansion.

MSC:

32A05 Power series, series of functions of several complex variables
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
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