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Fourier coefficients associated with the Riemann zeta-function
Karpatsʹkì Matematičnì Publìkacìï, 2016 We study the Riemann zeta-function $\zeta(s)$ by a Fourier series method. The summation of $\log|\zeta(s)|$ with the kernel $1/|s|^{6}$ on the critical line $\mathrm{Re}\; s = \frac{1}{2}$ is the main result of our investigation.
Yu.V. Basiuk, S.I. Tarasyuk
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Discrete Fourier transform and permutations [PDF]
Bulletin of the Polish Academy of Sciences: Technical Sciences, 2019 It is well known that the magnitudes of the coefficients of the discrete Fourier transform (DFT) are invariant under certain operations on the input data. In this paper, the effects of rearranging the elements of an input data on its DFT are studied.
S. Hui, S.H. Żak
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Karpatsʹkì Matematičnì Publìkacìï, 2015 The subclass of a zero order entire function $f$ is pointed out for which the existence of angular $\upsilon$-density for zeros of entire function of zero order is equivalent to convergence in $L^p[0,2\pi]$-metric of its logarithmic derivative.
M.R. Mostova, M.V. Zabolotskyj
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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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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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Fourier coefficients and growth of harmonic functions
International Journal of Mathematics and Mathematical Sciences, 1987 We consider Harmonic Functions, H of several variables. We obtain necessary and sufficient conditions on its Fourier coefficients so that H is an entire harmonic (that is, has no finite singularities) function; the radius of harmonicity in terms of its ...
A. fryant, H. Shankar
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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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Changing Signs of Fourier Coefficients [PDF]
Pacific Journal of Mathematics, 1965 In this chapter we shall be concerned with some remarkable facts concerning not one Fourier series $$ \sum\limits_{{{\text{n}} \in {\text{Z}}}} {\hat{f}(n){e^{{{\text{inx}}}}}}, $$ but rather “most” series $$ \sum\limits_{{{\text{n}} \in {\text{Z}}}} {\pm \hat{f}(n){e^{{{\text{inx}}}}}} $$ of the family obtained by making random changes ...
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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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