arXiv subjects

Stefan Tutić

Publications and source records attributed to Stefan Tutić.

4 recordsLinked to original sources

arXiv2026

On the pullback on spaces of distributions with prescribed microregularity with respect to a general Banach space

We consider the space $\mathcal{D}'^E_L(U)$ of all distributions on the open set $U$ whose wave front set measured with respect to a Banach space $E$ lies in a closed conic subset $L$ of $U\times(\mathbb{R}^n\backslash\{0\})$. The Banach space $E$ only satisfies mild technical assumptions. We show that the pullback by a diffeomorphism $f:O\rightarrow U$ is a topological isomorphism $f^*:\mathcal{D}'^E_L(U)\rightarrow\mathcal{D}'^E_{f^*L}(O)$. In the case when $E$ is the $L^p$-Sobolev space $W^{r,p}(\mathbb{R}^n)$ of order $r\in\mathbb{R}$, we study the pullback by a smooth map $f:O\rightarrow U$ of constant rank.

math.FA↗

arXiv2026

Extending wavelet regularity beyond Gevrey classes

We construct a smooth orthonormal wavelet $ψ$ such that both $ψ$ and its Fourier transform $\widehatψ$ belong to the extended Gevrey class $\mathcal{E}_σ(\mathbb{R})$ for $σ> 1$, providing an example that lies beyond all classical Gevrey classes. Our approach uses the idea of invariant cycles to extend the initial Lemarié-Meyer support of the low-pass filter $m_0$ from $ [-\frac{2π}{3}, \frac{2π}{3}]$ to $ [-\frac{4π}{5}, \frac{4π}{5}]$. This extension allows us to control the decay rate of $m_0$ near $\frac{2π}{3}$, which yields global decay estimates for $ψ$ and $\hatψ$. In addition, the decay rates are described using special functions involving the Lambert W function, which plays an important role in our construction.

math.FA↗

arXiv2025

On the continuity of the product of distributions in local Sobolev spaces

We consider the space $\mathscr{H}_L ^{s,r} (O)$ consisting of all local Sobolev distributions of order $s$ on an open set $O$ whose Sobolev wave front set of order $r$ is contained in the closed conic set $L\subseteq O\times(\mathbb{R}^m\backslash\{0\})$. We introduce a locally convex topology on $\mathscr{H}_L ^{s,r} (O)$ and show that the ordinary product of smooth functions uniquely extends to a continuous bilinear mapping $\mathscr{H}_{L_1} ^{r_1,r'} (O) \times \mathscr{H}_{L_2} ^{r_2,r''} (O) \to \mathscr{H}_{L} ^{s,r} (O)$, for appropriate $s$ and $r$ when $L_1$ and $L_2$ are in a favorable position. The key ingredient in our proof is to employ Hörmander's idea of considering the pullback by the diagonal map $x\mapsto (x,x)$ of the tensor product of two distributions.

math.FA↗

arXiv2024

Band-limited wavelets beyond Gevrey regularity

It is known that a smooth function of exponential decay at infinity can not be an orthonormal wavelet. Dziubański and Hernández constructed smooth orthonormal wavelets of Gevrey type subexponential decay. We weaken the Gevrey type decay and construct orthonormal wavelets of subexponential decay related to the so-called extended Gevrey classes. The virtue of our construction is that prescise asymptotics of functions from such classes can be given in terms of the Lambert $W$ function.

math.FA↗