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### A class of Fourier series

Colloquium Mathematicae

Acta Arithmetica

### A formula for the number of solutions of a restricted linear congruence

Mathematica Bohemica

Consider the linear congruence equation ${x}_{1}+...+{x}_{k}\equiv b\phantom{\rule{4.44443pt}{0ex}}\left(mod\phantom{\rule{0.277778em}{0ex}}{n}^{s}\right)$ for $b\in ℤ$, $n,s\in ℕ$. Let ${\left(a,b\right)}_{s}$ denote the generalized gcd of $a$ and $b$ which is the largest ${l}^{s}$ with $l\in ℕ$ dividing $a$ and $b$ simultaneously. Let ${d}_{1},...,{d}_{\tau \left(n\right)}$ be all positive divisors of $n$. For each ${d}_{j}\mid n$, define ${𝒞}_{j,s}\left(n\right)=\left\{1\le x\le {n}^{s}:{\left(x,{n}^{s}\right)}_{s}={d}_{j}^{s}\right\}$. K. Bibak et al. (2016) gave a formula using Ramanujan sums for the number of solutions of the above congruence equation with some gcd restrictions on ${x}_{i}$. We generalize their result with generalized gcd restrictions on ${x}_{i}$ and prove that for the above linear congruence, the number of solutions...

### A new extension of monotone sequences and its applications.

JIPAM. Journal of Inequalities in Pure &amp; Applied Mathematics [electronic only]

### A note on a theorem of Boas

Matematički Vesnik

### A note on Fourier coefficients

Rendiconti del Seminario Matematico della Università di Padova

### A Note on Lipschitz Classes.

Mathematische Zeitschrift

### A note on rearrangements of Fourier coefficients

Annales de l'institut Fourier

Let $f\left(x\right)\sim \Sigma {a}_{n}{e}^{2\pi inx},f*\left(x\right)\sim {\sum }_{n=0}^{\infty }a{*}_{n}\phantom{\rule{0.166667em}{0ex}}\mathrm{cos}\phantom{\rule{0.166667em}{0ex}}2\pi nx$, where the $a{*}_{n}$ are the numbers $|{a}_{n}|$ rearranged so that ${a}_{n}^{*}↘0$. Then for any convex increasing $\psi$, $\parallel \psi \left(|f{|}^{2}{\parallel }_{1}\le \parallel \psi \left(20|f*{|}^{2}{\parallel }_{1}$. The special case $\psi \left(t\right)={t}^{q/2}$, $q\ge 2$, gives $\parallel f{\parallel }_{q}\le 5\parallel f*{\parallel }_{q}$ an equivalent of Littlewood.

### A remark on entropy of Abelian groups and the invariant uniform approximation property

Studia Mathematica

### A simple observation about compactness and fast decay of Fourier coefficients.

Annals of Functional Analysis (AFA) [electronic only]

### A study of the real Hardy inequality.

JIPAM. Journal of Inequalities in Pure &amp; Applied Mathematics [electronic only]

### A theorem for Fourier coefficients of a function of class ${L}^{p}$.

International Journal of Mathematics and Mathematical Sciences

### A theorem of Cesari on mulitple Fourier series

Studia Mathematica

### A variation norm Carleson theorem

Journal of the European Mathematical Society

We strengthen the Carleson-Hunt theorem by proving ${L}^{p}$ estimates for the $r$-variation of the partial sum operators for Fourier series and integrals, for $r>\mathrm{𝚖𝚊𝚡}\left\{{p}^{\text{'}},2\right\}$. Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory.

### Addition au mémoire sur les fonctions discontinues

Annales scientifiques de l'École Normale Supérieure

### Algebrability of the set of non-convergent Fourier series

Studia Mathematica

We show that, given a set E ⊂ 𝕋 of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t ∈ E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra of 𝓒(𝕋) every non-zero element of which has a Fourier series expansion divergent in E.

### An application of interpolation theory to Fourier series

Studia Mathematica

### An approximation problem in ${L}^{p}\left(\left[0,2\pi \right]\right)$, 2 < p < ∞

Studia Mathematica

### An estimate of the Fourier coefficients of functions belonging to the Besov class.

Publications de l'Institut Mathématique. Nouvelle Série

### An extension of the Riemann-Lebesgue lemma and some applications.

Acta Universitatis Apulensis. Mathematics - Informatics

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