Vol. 103, No. 2, 1982

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A Fourier transform theorem on nilmanifolds and nil-theta functions

Richard Cole Penney

Vol. 103 (1982), No. 2, 539–568

A theorem describing the image of the Euclidean Fourier transform on certain nilmanifolds is proven. As an application, we compute the Fourier transform of a certain class of distributions on a manifold which is analogous with the class of classical theta functions on C. It is shown that our theta functions satisfy a functional equation which generalizes the functional equation satisfied by the Jacobi theta functions.

Mathematical Subject Classification 2000
Primary: 22E30
Secondary: 14K25, 22E25
Received: 15 January 1980
Published: 1 December 1982
Richard Cole Penney