Abstract
In a recent paper [2],2 W. Magnus has shown that analogues of the Fourier inversion and Plancherel theorems hold for matrix-valued functions on the real line R. We propose to show that these theorems actually hold for an arbitrary locally compact Abelian group, and that Magnus’s inversion integral (1. c. (1.4)) can be simplified. For all group- and integral-theoretic notation, terms, and facts used here without explanation, see [1].
The first-named author is a fellow of the John Simon Guggenheim Memorial Foundation.
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Bibliography
Lynn H. Loomis, An introduction to abstract harmonic analysis, New York, Van Nostrand, 1953.
Wilhelm Magnus, A Fourier theorem for matrices, Proc. Amer. Math. Soc. vol. 6 (1955) pp. 880–890. (Also appeared as Division of Electromagnetic Research, Institute of Mathematical Sciences, New York University, Research Report No. BR-8 (1954)).
Received by the editors February 16, 1956 and, in revised form, October 1, 1956.
Numbers in brackets refer to the bibliography.
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© 1993 Springer-Verlag Berlin Heidelberg
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Hewitt, E., Wigner, E.P. (1993). On a Theorem of Magnus. In: Wightman, A.S. (eds) The Collected Works of Eugene Paul Wigner. The Collected Works of Eugene Paul Wigner, vol A / 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02781-3_37
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DOI: https://doi.org/10.1007/978-3-662-02781-3_37
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