Zobrazeno 1 - 10
of 314
pro vyhledávání: '"VINDAS, Jasson"'
This article generalizes the results of [J. Math. Anal. Appl. 512 (2022), Article No. 126075], which presented a theory of distributions (generalized functions) with a singular curve contained in the domain of the test functions. In this present arti
Externí odkaz:
http://arxiv.org/abs/2408.02864
We study approximation properties of the Fr\'{e}chet space of all continuously differentiable functions $\tau$ such that $\tau'(x)=o(1)$ and such that their Laplace transforms admit entire extensions to $\mathbb{C}$. As an application, these approxim
Externí odkaz:
http://arxiv.org/abs/2407.15547
Let $\mathcal H$ be a Hilbert space of distributions on $\mathbf R^d$ which contains at least one non-zero element in $\mathscr D '(\mathbf R^d)$. If there is a constant $C_0>0$ such that $$ \nm {e^{i\scal \cdo \xi}f(\cdo -x)}{\mathcal H}\le C_0\nm f
Externí odkaz:
http://arxiv.org/abs/2407.08435
We study inclusion relations between Gelfand-Shilov type spaces defined via a weight (multi-)sequence system, a weight function system, and a translation-invariant Banach function space. We characterize when such spaces are included into one another
Externí odkaz:
http://arxiv.org/abs/2407.06126
Autor:
Vindas, Jasson
We show that the sum function of the M\"{o}bius function of a Beurling number system must satisfy the asymptotic bound $M(x)=o(x)$ if it satisfies the prime number theorem and its prime distribution function arises from a monotone perturbation of eit
Externí odkaz:
http://arxiv.org/abs/2406.00736
We establish Hermite expansion characterizations for several subspaces of the Fr\'{e}chet space of functions on the real line satisfying \begin{equation*} |f(x)| \lesssim e^{-(\frac{1}{2} - \lambda ) x^{2}} , \qquad | \widehat{f}(\xi )| \lesssim e^{-
Externí odkaz:
http://arxiv.org/abs/2405.03282
We prove that the spaces of smooth and ultradifferentiable vectors associated with a representation of a real Lie group on a Fr\'{e}chet space $E$ are quasinormable if $E$ is so. A similar result is shown to hold for the linear topological invariant
Externí odkaz:
http://arxiv.org/abs/2403.08296
Autor:
Chen, Bin, Vindas, Jasson
We establish new versions of the Wiener-Ikehara theorem where only boundary assumptions on the real part of the Laplace transform are imposed. Our results generalize and improve a recent theorem of T. Koga [J. Fourier Anal. Appl. 27 (2021), Article N
Externí odkaz:
http://arxiv.org/abs/2311.03013
We study the range of validity of the density hypothesis for the zeros of $L$-functions associated with cusp Hecke eigenforms $f$ of even integral weight and prove that $N_{f}(\sigma, T) \ll T^{2(1-\sigma)+\varepsilon}$ holds for $\sigma \geq 1407/16
Externí odkaz:
http://arxiv.org/abs/2310.14797
Publikováno v:
Monatsh. Math. 201 (2023), 483-498
We introduce and study new modules and spaces of generalized functions that are related to the classical Besov spaces. Various Schwartz distribution spaces are naturally embedded into our new generalized function spaces. We obtain precise criteria fo
Externí odkaz:
http://arxiv.org/abs/2204.13012