Results 31 to 40 of about 3,568,332 (307)
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 ...
openaire +2 more sources
Smoothness of functions and Fourier coefficients
Sbornik. Mathematics, 2019 We consider functions represented as trigonometric series with general monotone Fourier coefficients. The main result of the paper is the equivalence of the modulus of smoothness, , of such functions to certain sums of their Fourier coefficients.
M. Dyachenko, A. Mukanov, S. Tikhonov
semanticscholar +1 more source
Fourier coefficients for theta representations on covers of general linear groups [PDF]
Transactions of the American Mathematical Society, 2016 We show that the theta representations on certain covers of general linear groups support certain types of unique functionals. The proof involves two types of Fourier coefficients.
Yuanqing Cai
semanticscholar +1 more source
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.
openaire +1 more source
Efficient Fourier Single-Pixel Imaging with Gaussian Random Sampling
Photonics, 2021 Fourier single-pixel imaging (FSI) is a branch of single-pixel imaging techniques. It allows any image to be reconstructed by acquiring its Fourier spectrum by using a single-pixel detector.
Ziheng Qiu +5 more
doaj +1 more source
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
openaire +1 more source
Süleyman Demirel Üniversitesi Fen-Edebiyat Fakültesi Fen Dergisi, 2023 In this paper, differential-differential difference equations with variable coefficients have been solved using the Fourier Transform Method (FTM). In addition, new definitions and theorems are introduced.
Sunnet Avezov, Murat Düz, Ahmad Issa
doaj +1 more source
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 ...
openaire +4 more sources
Journal of Function Spaces, 2017 For a bivariate function on a square, in general, its Fourier coefficients decay slowly, so one cannot reconstruct it by few Fourier coefficients. In this paper we will develop a new approximation scheme to overcome the weakness of Fourier approximation.
Zhihua Zhang
doaj +1 more source
On the Fourier coefficients of negative index meromorphic Jacobi forms [PDF]
, 2015 In this paper, we consider the Fourier coefficients of meromorphic Jacobi forms of negative index. This extends recent work of Creutzig and the first two authors for the special case of Kac–Wakimoto characters which occur naturally in Lie theory and ...
K. Bringmann, Larry Rolen, S. Zwegers
semanticscholar +1 more source