Weighted L(R)→ L(R) Fourier inequalities are studied. We prove Pitt–Boas type results on integrability with general weights of the Fourier transform of a radial function.

By sampling the window of a Gabor frame for L(R) belonging to Feichtinger’s algebra, S0(R), one obtains a Gabor frame for l(Z). In this article we present a survey of results by R. Orr and A.J.E.M. Janssen and extend their ideas to cover interrelations among Gabor frames for the four spaces L(R), l(Z), L([0, L]) and C. Some new results about general dual windows with respect to sampling and per...

Sürdürülebilirlik hiç olmad??? kadar önem kazanm??t?r. Firmalar da bu kapsamda çe?itli kurumsal sosyal sorumluluk (KSS) faaliyetleri gerçekle?tirmektedir. Bu faaliyetlerin payda?lar üzerindeki etkileri ise hem yaz?nda uygulamada ilgi uyand?rmaktad?r. Buna kar??n KSS haberleri ile ilgili çok k?s?tl? say?da çal??ma bulunmas? ve bunlar?n hiçbirinin ürün üretim süreç haberlerini kapsamamas? çal??ma...

Here we provide a unifying treatment of the convergence general form sampling type operators, given by so-called Durrmeyer series. In particular pointwise and uniform theorem on $\mathbb{R}$, in this context also furnish quantitative estimate for order approximation, using modulus continuity function to be approximated. Then obtain modular setting Orlicz spaces $L^\varphi(\mathbb{R})$. From lat...

The first nontrivial zeroes of the Riemann ζ function are ≈ 1 2 ± 14.13472i. We investigate the question of whether or not any other Lfunction has a higher lowest zero. To do so we try to quantify the notion that the L-function of a “small” automorphic representation (i.e. one with small level and archimedean type) does not have small zeroes, and vice-versa. We prove that many types of automorp...

In this paper we consider the regularity problem of Navier–Stokes equations in $$ {\mathbb {R}}^{3} . We show that Serrin-type condition imposed on one component velocity u_3\in L^p(0,T; L^q({\mathbb ))$$ with \frac{2}{p}+ \frac{3}{q} <1$$ , 3<q \le +\infty implies weak Leray solution u: \times (0,T) \rightarrow initial data belonging to L^2({\mathbb {R}}^3) \cap L^3({\mathbb {R}}^{3})$$ The re...

Inductive bintree : Set := | Leaf: bintree | Node: bintree -> bintree -> bintree. In the following, I also use some definitions of the Coq library. Type nat is type of Peano numbers generated from O and S. Type Z is type of infinite binary integers (more efficient than nat to perform large concrete computations). At last, list is the polymorphic type of lists. The Coq definition of enumBT is gi...

We study the question whether characteristic functions of strictly convex compact sets with smooth boundaries in R are L × L → L bounded bilinear Fourier multiplier operators on R × R. When n ≥ 2 we answer this question in the negative outside the local L case, i.e., when 1/p + 1/q = 1/r and 2 ≤ p, q, r′ <∞ fails. Our proof is based on a suitable adaptation of the Kakeya type construction emplo...