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On a Sequence of Fourier Coefficients [PDF]
Proceedings of the American Mathematical Society, 1956 Let \(B_{n}(x)\) be the \(n\)-th term of the conjugate Fourier series of \(f(x),\) and let \(\psi(t)=f(x+t)-f(x-t)-l\). The author shows that if \[ \Psi(t)=\int_{0}^{t}\psi(u)du=o(t) \text{ and } \int_{\varepsilon}^{\delta}\frac{|\psi(t+\epsilon)-\psi(t)|}{t}dt\rightarrow 0 \] as \(\varepsilon\rightarrow 0\) for some fixed \(\delta\), then the sequence
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Two-point boundary value problem for a partial differential equation in spaces of periodic functions
Математичні Студії, 2020 We investigate the two-point in time boundary value problem for the partial differential equations of the second-order with one spatial variable and constant coefficients. The problem is considered in in the spaces of functions which Fourier coefficients
V.S. Ilkiv +3 more
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A method to derive Fourier–wavelet spectra for the characterization of global-scale waves in the mesosphere and lower thermosphere and its MATLAB and Python software (fourierwavelet v1.1) [PDF]
Geoscientific Model Development, 2023 This paper describes a simple method for characterizing global-scale waves in the mesosphere and lower thermosphere (MLT), such as tides and traveling planetary waves, using uniformly gridded two-dimensional longitude–time data.
Y. Yamazaki
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Journal of Mathematics and Physics, 1943 Koeffizienten bezüglich \(x^k\) für \(k = 0\,(1)\,10\) und \(n = 1\,(1)\,100\) mit 10 D.
Lowan, Arnold N., Laderman, Jack
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Karpatsʹkì Matematičnì Publìkacìï, 2020 Let $f$ be an entire function of order $\rho\in (0,+\infty)$ with zeros on a finite system of rays $\{z: \arg z=\psi_{j}\}$, $j\in\{1,\ldots,m\}$, $0\le ...
R.V. Khats'
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ON FOURIER COEFFICIENTS OF MODULAR FORMS [PDF]
Bulletin of the Australian Mathematical Society, 2010 AbstractRecursive formulae satisfied by the Fourier coefficients of meromorphic modular forms on groups of genus zero have been investigated by several authors. Bruinieret al. [‘The arithmetic of the values of modular functions and the divisors of modular forms’,Compositio Math.140(3) (2004), 552–566] found recurrences for SL(2,ℤ); Ahlgren [‘The theta ...
Cummins, C. J., Haghighi, N. S.
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Modified Fourier expansions: theory, construction and applications [PDF]
, 2010 Modified Fourier expansions present an alternative to more standard algorithms for the approximation of nonperiodic functions in bounded domains. This thesis addresses the theory of such expansions, their effective construction and computation, and ...
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Radar matched filtering using the fractional fourier transform [PDF]
, 2010 -A matched filter is the optimal linear filter for maximizing the signal to noise ratio (SNR) in the presence of additive noise. Matched filters are commonly used in radar systems where the transmitted signal is known and may be used as a replica to be ...
Clemente, Carmine +2 more
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Obtaining the Fourier spectrum via Fourier coefficients [PDF]
The Fourier spectrum is a family of dimensions that interpolates between the Fourier and Hausdorff dimensions and is defined in terms of certain energies which capture Fourier decay.
Carnovale, Marc +2 more
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Transformations of Fourier coefficients [PDF]
Proceedings of the American Mathematical Society, 1952 Introduction. In 1923 M. Fekete [2]2 introduced the concept of factor sequences that left invariant the class of a Fourier series. That is, Fekete investigated the conditions to which a sequence of constants (X„) must be subjected in order that (X„a„, X„i„) be Fourier coefficients of a function of the same class, K, as that of the function determined ...
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