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Jasson Vindas

Publications and source records attributed to Jasson Vindas.

At least 19 recordsLinked to original sources
arXiv2026

Spectral characterizations of stable operator semigroups

We introduce the notion of local pseudofunction spectrum $\sigma_{PF}(A)$ for the infinitesimal generator $A$ of a bounded $C_0$-semigroup $\mathcal{T} = (T(t))_{t \geq 0}$ on a Banach space $X$ and show it is the right spectral concept to deliver a full characterization of the strong stability of $\mathcal{T}$: $$ \forall x \in X : ~ \lim_{t \to \infty} \| T(t) x \|_X = 0 \quad \Longleftrightarrow \quad \sigma_{PF}(A) = \varnothing. $$ We demonstrate how this yields a quick proof of the well-known Arendt-Batty-Lyubich-V\~u theorem and establish novel stability results through local range density conditions for semigroups whose local pseudofunction spectra are a null subset of the imaginary axis. We also obtain similar stability characterization theorems for individual orbits and for semi-uniform stability. As an application of our results, we provide spectral characterizations of almost periodic $C_0$-semigroups with countable spectrum. In addition, we prove optimal Tauberian theorems of Katznelson-Tzafriri type and discuss connections with Wiener kernels.

math.FA↗
arXiv2026

A Wiener-Ikehara type theorem and its application to Chebyshev bounds for Beurling primes

We provide a new version of the Wiener-Ikehara theorem where one deduces bounds $$ 0< \liminf_{x\to\infty} \frac{S(x)}{e^{x}}\leq \limsup_{x\to\infty} \frac{S(x)}{e^{x}} <\infty $$ for (in particular) a non-decreasing function $S$ from a mild hypothesis on the boundary behavior of its Laplace transform on a vertical segment containing $s=1$. As an application, we establish new criteria for the validity of Chebyshev bounds for Beurling generalized prime number systems under weaker conditions than were known so far.

math.NT↗
arXiv2025

Optimal decay of semi-uniformly stable operator semigroups with empty spectrum

We show that it is impossible to quantify the decay rate of a semi-uniformly stable operator semigroup based on sole knowledge of the spectrum of its infinitesimal generator. More precisely, given an arbitrary positive function $r$ vanishing at $\infty$, we construct a Banach space $X$ and a bounded semigroup $ (T(t))_{t \geq 0}$ of operators on it whose infinitesimal generator $A$ has empty spectrum $σ(A)=\varnothing$, but for which, for some $x \in X$, $$ \limsup_{t\to\infty} \frac{\|T(t)A^{-1}x\|_{X}}{r(t)}=\infty. $$

math.FA↗
arXiv2025

Quantitative uncertainty principles for time-frequency Gaussian decay

For real symmetric positive definite matrices $A$ and $B$, we characterize when a function $f \in L^2(\mathbb{R}^d)$ satisfies \[ |f(x)| \lesssim e^{-(\frac12 - λ) \langle Ax, x\rangle} \quad \text{and} \quad |\widehat{f}(ξ)| \lesssim e^{-(\frac12 - λ) \langle Bξ, ξ\rangle} , \qquad \forall λ> 0 , \] or even more specified time-frequency decay estimates, in terms of the skewed Hermite series expansion of $f$. We also consider coordinate-wise time-frequency decay and determine when it becomes equivalent to the same bounds on the skewed Hermite coefficients.

math.FA↗
arXiv2025

On the inclusion relations between Gelfand-Shilov spaces

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 in terms of growth relations for the defining weight sequence and function systems. Our general framework allows for a unified treatment of the Gelfand-Shilov spaces $\mathcal{S}^{[M]}_{[A]}$ (defined via weight sequences $M$ and $A$) and the Beurling-Björck spaces $\mathcal{S}^{[ω]}_{[η]}$ (defined via weight functions $ω$ and $η$).

math.FA↗
arXiv2025

On a space of functions with entire Laplace transforms and its connection with the optimality of the Ingham-Karamata theorem

We study approximation properties of the Fréchet space of all continuously differentiable functions $τ$ such that $τ'(x)=o(1)$ and such that their Laplace transforms admit entire extensions to $\mathbb{C}$. As an application, these approximation results are combined with the open mapping theorem to show the optimality theorem for the Ingham-Karamata Tauberian theorem.

math.CA↗
arXiv2025

Non-isometric translation and modulation invariant Hilbert spaces

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 $$ \nm {e^{i\scal \cdo ξ}f(\cdo -x)}{\mathcal H}\le C_0\nm f{\mathcal H}, \qquad f\in \mathcal H ,\ x,ξ\in \mathbf R^d, $$ then we prove that $\maclH = L^2(\mathbf R^d)$, with equivalent norms.

math.FA↗
arXiv2025

Distributions in spaces with thick submanifolds

We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test functions may be singular. We define several operations, including ``thick partial derivatives'', and clarify their connection with their classical counterparts in Schwartz distribution theory. We also introduce and study a number of special thick distributions, including new thick delta functions, or more generally thick multilayer distributions along a submanifold.

math.FA↗
arXiv2024

Hermite expansions for spaces of functions with nearly optimal time-frequency decay

We establish Hermite expansion characterizations for several subspaces of the Fréchet space of functions on the real line satisfying \begin{equation*} |f(x)| \lesssim e^{-(\frac{1}{2} - λ) x^{2}} , \qquad | \widehat{f}(ξ)| \lesssim e^{-(\frac{1}{2} - λ) ξ^{2}} , \qquad \forall λ> 0 . \end{equation*} In particular, we extend and improve Fourier characterizations of the so-called proper Pilipović spaces obtained in [J. Funct. Anal. 284 (2023), 109724]. The main ingredients in our proofs are the Bargmann transform and some achieved optimal forms of the Phragmén-Lindelöf principle.

math.FA↗
arXiv2024

On the estimate $M(x)=o(x)$ for Beurling generalized numbers

We show that the sum function of the Möbius 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 either the classical prime numbers or the logarithmic integral.

math.NT↗
arXiv2024

A new generalized prime random approximation procedure and some of its applications

We present a new random approximation method that yields the existence of a discrete Beurling prime system $\mathcal{P}=\{p_{1}, p_{2}, \dotso\}$ which is very close in a certain precise sense to a given non-decreasing, right-continuous, nonnegative, and unbounded function $F$. This discretization procedure improves an earlier discrete random approximation method due to H. Diamond, H. Montgomery, and U. Vorhauer [Math. Ann. 334 (2006), 1-36], and refined by W.-B. Zhang [Math. Ann. 337 (2007), 671-704]. We obtain several applications. Our new method is applied to a question posed by M. Balazard concerning Dirichlet series with a unique zero in their half plane of convergence, to construct examples of very well-behaved generalized number systems that solve a recent open question raised by T. Hilberdink and A. Neamah in [Int. J. Number Theory 16 05 (2020), 1005-1011], and to improve the main result from [Adv. Math. 370 (2020), Article 107240], where a Beurling prime system with regular primes but extremely irregular integers was constructed.

math.NT↗
arXiv2024

Vector valued Hardy spaces related to analytic functions having distributional boundary values

The Hardy space $H^{p}$ of vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ and with values in Banach space are defined. Vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ with values in Hilbert space and which have vector valued tempered distributions as boundary value are proved to be in $H^{p}$ corresponding to Hilbert space if the boundary value is in $L^{p}$ with values in Hilbert space. A Poisson integral representation for such vector valued analytic functions is obtained.

math.FA↗
arXiv2024

On the density hypothesis for $L$-functions associated with holomorphic cusp forms

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 $N_{f}(σ, T) \ll T^{2(1-σ)+\varepsilon}$ holds for $σ\geq 1407/1601$. This improves upon a result of Ivić, who had previously shown the zero-density estimate in the narrower range $σ\geq 53/60$. Our result relies on an improvement of the large value estimates for Dirichlet polynomials based on mixed moment estimates for the Riemann zeta function. The main ingredients in our proof are the Halász-Montgomery inequality, Ivić's mixed moment bounds for the zeta function, Huxley's subdivision argument, Bourgain's dichotomy approach, and Heath-Brown's bound for double zeta sums.

math.NT↗
arXiv2024

Quasinormability and property $(\Omega)$ for spaces of smooth and ultradifferentiable vectors associated with Lie group representations

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 $(\Omega)$. In the ultradifferentiable case, our results particularly apply to spaces of Gevrey vectors of Beurling type. As an application, we study the quasinormability and the property $(\Omega)$ for a broad class of Fr\'{e}chet spaces of smooth and ultradifferentiable functions on Lie groups globally defined via families of weight functions.

math.FA↗
arXiv2023

Generalizations of Koga's version of the Wiener-Ikehara theorem

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 No. 18]. As an application, we give a quick Tauberian proof of Blackwell's renewal theorem.

math.CV↗