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pro vyhledávání: '"42A16"'
The purpose of the present paper is to address multiple aspects of the Fuglede question dealing (Fourier spectra vs geometry) with a variety of $L^2$ contexts where we make precise the interplay between the three sides of the question: (i) existence
Externí odkaz:
http://arxiv.org/abs/2410.03587
In this paper, we use Clifford algebra $Cl_{2,0}$ to find the 2D orbit of Hydrogen electron under a Coulomb force and a perturbing circularly polarized electric field of light at angular frequency~$\omega$, which is turned on at time $t = 0$ via a un
Externí odkaz:
http://arxiv.org/abs/2410.00056
Autor:
Berner, Chad, Weber, Eric S.
Frames in a Hilbert space that are generated by operator orbits are vastly studied because of the applications in dynamic sampling and signal recovery. We demonstrate in this paper a representation theory for frames generated by operator orbits that
Externí odkaz:
http://arxiv.org/abs/2409.10706
Consider the set $E(D, N)$ of all bivariate exponential polynomials $$ f(\xi, \eta) = \sum_{j=1}^n p_j(\xi, \eta) e^{2\pi i (x_j\xi+y_j\eta)}, $$ where the polynomials $p_j \in \mathbb{C}[\xi, \eta]$ have degree $
Externí odkaz:
http://arxiv.org/abs/2409.01432
We determine the generic multiplicative approximation rate on a hypersurface. There are four regimes, according to convergence or divergence and curved or flat, and we address all of them. Using geometry and arithmetic in Fourier space, we develop a
Externí odkaz:
http://arxiv.org/abs/2408.10911
Autor:
Casper, W. Riley, Yakimov, Milen
We investigate the restriction of the discrete Fourier transform $F_N : L^2(\mathbb{Z}/N \mathbb{Z}) \to L^2(\mathbb{Z}/N \mathbb{Z})$ to the space $\mathcal C_a$ of functions with support on the discrete interval $[-a,a]$, whose transforms are suppo
Externí odkaz:
http://arxiv.org/abs/2407.20379
Autor:
Serdyuk, Anatolii, Shidlich, Andrii
This review paper highlights the main aspects of the development of research related to the solution of extreme problems in the theory of approximation in the spaces ${\mathcal S}^p$ and $B{\mathcal S}^p$ of periodic and almost periodic summable func
Externí odkaz:
http://arxiv.org/abs/2407.04329
Autor:
Stefanescu, Eduard
Let $(a_n)_{n \in \mathbb{N}}$ be a Hadamard lacunary sequence. We give upper bounds for the maximal gap of the set of dilates $\{a_n \alpha\}_{n \leq N}$ modulo 1, in terms of $N$. For any lacunary sequence $(a_n)_{n \in \mathbb{N}}$ we prove the ex
Externí odkaz:
http://arxiv.org/abs/2406.19802
Autor:
Derevianko, Nadiia
In the paper, we develop a new method for the recovery of rational functions. Our idea is based on the property that Fourier coefficients of rational functions have the exponential structure and reconstruction of this exponential structure with the E
Externí odkaz:
http://arxiv.org/abs/2406.13192
Autor:
Nicholson, Martin
This is a discussion of miscellaneous summation, integration and transformation formulas obtained using Fourier analysis. The topics covered are: Series of the form $\sum_{n\in\mathbb{Z}} c_ne^{\pi i \gamma n^2}$; Fusion of integrals, and in particul
Externí odkaz:
http://arxiv.org/abs/2404.10805