§0. Introduction §1. The Scheme-Theoretic Fourier Transform §2. Discrete Gaussians and Gauss Sums §3. Review of Degree Computations in [HAT] §4. The Fourier Transform of an Algebraic Theta Function: The Case of an Étale Lagrangian Subgroup §5. The Fourier Transform of an Algebraic Theta Function: The Case of a Lagrangian Subgroup with Nontrivial Multiplicative Part §6. Generic Properties of the...

provided an = sin (wn/2) and k(x) =sin (irx/2). Weinberger [8] treated the case when the coefficients a„ form a periodic sequence; that is an+q = a„ for some integer q. Making use of the character theory of Dirichlet 7-functions, he found the conditions on the a„ so that (3) holds with the kernel (2/q112) cos (2irx/q) or the kernel (2/q112) sin (2irx/q). (These kernels give self-reciprocal tran...

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...

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...

Here sn x is an abbreviation for sin (wx/2). This paper gives other conditions for the validity of these identities. The previous conditions permitted to have various types of discontinuity. The present paper is concerned with smooth functions; however, the growth at 0 and «> is permitted to be greater than before. Theorems 1, 2, and 3 of the previous paper together with Theorems 2 and 3 of...

The paper is devoted to the investigation of problem approximation continuous periodic functions by trigonometric polynomials, which are generated linear methods summation Fourier series.
 simplest example a partial sums their series. However, sequences not uniformly convergent over class functions. Therefore, many studies research approximative properties methods, transformations series a...

By using the Fourier transform, we successfully give Kröger-type estimates for sums of eigenvalues free plate (under tension and with nonzero Poisson’s ratio) in terms dimension ambient space, volume domain, parameter ratio.