» 3-handle construction on II$_1$ factors
04/04/25 09:00 from math.OA updates on arXiv.org
arXiv:2504.02003v1 Announce Type: new Abstract: We find a subtle modification to the construction of Chifan-Ioana-Kunnawalkam Elayavalli, which yields a drastic simplification of the proof of the existence of two non Gamma non elementari...

» Generalised Haj{\l}asz-Besov spaces on $RD$-spaces
04/04/25 09:00 from math.FA updates on arXiv.org
arXiv:2504.02434v1 Announce Type: new Abstract: An $RD$ space is a doubling measure metric space $\Omega$ with the additional property that it has a reverse doubling property. In this paper we introduce a new class of Haj{\l}asz-Besov sp...

» Spectral estimates for non-self-adjoint Dirac operators
04/04/25 09:00 from math.SP updates on arXiv.org
arXiv:2504.02236v1 Announce Type: new Abstract: The spectrum of a periodic non-self-adjoint Dirac operator is studied, and its explicit dependence on a semi-classical parameter is also considered. Using ``energy'' techniques several new ...

» Improved universal approximation with neural networks studied via affine-invariant subspaces of $L_2(\mathbb{R}^n)$
04/04/25 09:00 from math.FA updates on arXiv.org
arXiv:2504.02445v1 Announce Type: new Abstract: We show that there are no non-trivial closed subspaces of $L_2(\mathbb{R}^n)$ that are invariant under invertible affine transformations. We apply this result to neural networks showing tha...

» The growth of transcendental entire solutions of linear difference equations with polynomial coefficients
04/04/25 09:00 from math.CV updates on arXiv.org
arXiv:2504.02243v1 Announce Type: new Abstract: In this paper, we study the growth of transcendental entire solutions of linear difference equations \begin{equation} P_m(z)\Delta^mf(z)+\cdots+P_1(z)\Delta f(z)+P_0(z)f(z)=0,\tag{+} \end{e...

» Spectral asymmetry via pseudodifferential projections: the massless Dirac operator
04/04/25 09:00 from math.SP updates on arXiv.org
arXiv:2504.02336v1 Announce Type: cross Abstract: A new approach to the study of spectral asymmetry for systems of partial differential equations (PDEs) on closed manifolds was proposed in a recent series of papers by the first author an...

» Convergence of permuted products of exponentials
04/04/25 09:00 from math.FA updates on arXiv.org
arXiv:2504.02681v1 Announce Type: new Abstract: Let $\{A_{i,n}\}$ be a triangular array of elements in a Banach algebra, whose norms do not grow too fast, and whose row averages converge to $A$. Let $\sigma \in S(n)$ be a permutation dra...

» Behavior of Absorbing and Generating $p$-Robin Eigenvalues in Bounded and Exterior Domains
04/04/25 09:00 from math.SP updates on arXiv.org
arXiv:2408.06236v2 Announce Type: replace-cross Abstract: We establish rigorous quantitative inequalities for the first eigenvalue of the generalized $p$-Robin problem, for both the classical diffusion absorption case, where the Robin bo...