منابع مشابه
Ramanujan Duals and Automorphic Spectrum
We introduce the notion of the automorphic dual of a matrix algebraic group defined over Q . This is the part of the unitary dual that corresponds to arithmetic spectrum. Basic funcional properties of this set are derived and used both to deduce arithmetic vanishing theorems of "Ramanujan" type as well as to give a new construction of automorphic forms. Let G be a semisimple linear algebraic gr...
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Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high-dimensional Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property, and a pseudo-randomness result. For this purpose we prove a Cheeger-type inequality and a mixing lemma of independent interest.
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The Doppler spectrum estimation of a weather radar signal in a classic way can be made by two methods, temporal one based in the autocorrelation of the successful signals, whereas the other one uses the estimation of the power spectral density PSD by using Fourier transforms. We introduces a new tool of signal processing based on Ramanujan sums cq(n), adapted to the analysis of arithmetical seq...
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We show that the map from minimal-parabolic pseudo-Eisenstein series to their decomposition coefficients against minimal-parabolic Eisenstein series is an isometry to its image. The argument characterizing the image is sketched, but is incomplete without characterizing the other, less-continuous parts of the spectral decomposition. Thus, we do not quite prove Plancherel for this part of the spe...
متن کاملDoppler spectrum estimation by Ramanujan-Fourier Transform (RFT)
The Doppler spectrum estimation of a weather radar signal in a classic way can be made by two methods, temporal one based in the autocorrelation of the successful signals, whereas the other one uses the estimation of the power spectral density PSD by using Fourier transforms. We introduces a new tool of signal processing based on Ramanujan sums cq(n), adapted to the analysis of arithmetical seq...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1992
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1992-00267-7