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- W2055072064 abstract "1. Introduction. The Peter-Weyl theorem asserts that if G is a compact group, then the matrix elements of a complete system of inequivalent irreducible unitary representations form a complete orthogonal system of functions in the Hilbert space of complex-valued square-integrable functions on G. When G is the circle (the real numbers modulo 2wx), then the irreducible representations are all one-dimensional, and are, in fact, the functions exp (inx). The Peter-Weyl theorem, then, makes it possible to generalize the concept of Fourier series to arbitrary compact groups and it asserts the convergence in the mean of the Fourier series of a function in L2. Of course a sequence of functions may converge in the mean without converging at any point. For classical Fourier series there are several theorems concerning the pointwise convergence or summability of Fourier series. Two of the principal results of this type are Fejer's theorem which asserts the (C, 1) convergence of the Fourier series at a point of continuity and the Fejer-Lebesgue theorem" @default.
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- W2055072064 date "1953-02-01" @default.
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- W2055072064 title "Summability of Fourier series on the quaternions of norm one" @default.
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