Stationary fields with positive angle

A. Makagon and H. Salehi

Journal of Multivariate Analysis, 1987, vol. 22, issue 1, 106-125

Abstract: An analytic characterization of stationary fields with a positive angle between the vertical past and future, in the sense of Helson and Lowdenslager, is given. The connection between the positivity of the angle and the convergence of the Fourier series for certain functions is studied. The case where both vertical and horizontal angles are positive is discussed. An example showing the positivity of the vertical angle while the horizontal angle is zero is provided. Proofs depend on various characterizations of densities admitting a positive angle for the circle case.

Keywords: stationary; fields; past; and; future; angle; spectral; condition; for; positivity; of; angle (search for similar items in EconPapers)
Date: 1987
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