» Equivariant Steklov homogenisation and stability of spectral representations
12/10/26 09:00 from math.SP updates on arXiv.org
arXiv:2610.12725v1 Announce Type: new Abstract: We prove that isolated spectral clusters preserve their finite-group representation under equivariant spectral convergence. In particular, an irreducible limiting eigenspace cannot split in...

» H\"older Continuity and Boundedness of Composition Operators on Pluriharmonic $\alpha$-Bloch Spaces
12/10/26 09:00 from math.CV updates on arXiv.org
arXiv:2610.12487v1 Announce Type: new Abstract: In this paper, we study the metric properties of pluriharmonic $\alpha$-Bloch-type mappings $f=h+\overline{g}\in\mathcal{H}(\mathbb{B}^{n},\mathbb{C}^{n})$ on the unit ball $\mathbb{B}^{n}\...

» Singular Levi-flats and holomorphic foliations on projective spaces
12/10/26 09:00 from math.CV updates on arXiv.org
arXiv:2610.12497v1 Announce Type: new Abstract: We study codimension-one holomorphic foliations admitting invariant singular real-analytic Levi-flat varieties. Our main problem is to determine when the local meromorphic first integrals f...

» High-Index Asymptotics of Mathieu Spectral Gaps and Splittings
12/10/26 09:00 from math.SP updates on arXiv.org
arXiv:2610.12751v1 Announce Type: new Abstract: Consider the Mathieu operator $L=-d^2/dx^2+2a\cos(2x)$ for fixed $a\in\mathbb{C}\setminus\{0\}$. For large enough $n$, the periodic ($n$ even) or anti-periodic ($n$ odd) problem on $[0,\pi]...

» Asymptotic Root Dynamics under Repeated and Fractional Integration
12/10/26 09:00 from math.CV updates on arXiv.org
arXiv:2610.12498v1 Announce Type: new Abstract: Fix a polynomial $P(x)=\sum_{j=0}^{m}a_jx^j$ of degree $m$, and let $I_kP$ be its $k$-fold antiderivative with all integration constants zero. Borwein, Chen, and Dilcher proved that, after ...

» Quantitative spectral stability and sharp Fourier estimates for periodic CMV matrices with decaying perturbations
12/10/26 09:00 from math.SP updates on arXiv.org
arXiv:2610.12856v1 Announce Type: new Abstract: We study half-line CMV matrices whose Verblunsky coefficients are decaying perturbations of periodic sequences. We quantify the stability of fine properties of the absolutely continuous spe...

» A proof of Borcea's quadratic variance conjecture
12/10/26 09:00 from math.CV updates on arXiv.org
arXiv:2610.12499v1 Announce Type: new Abstract: Let $p$ be a complex polynomial of degree $n\ge2$, and let $\sigma_2(p)$ be the root mean square distance of its zeros from their centroid, including multiplicities. We prove that every zer...

» Wiener's lemma for quasicrystals: hull-uniform decay of covariant kernels on Delone sets
12/10/26 09:00 from math.OA updates on arXiv.org
arXiv:2610.12770v1 Announce Type: new Abstract: This paper studies continuous covariant kernel families over hulls of Delone sets of finite local complexity using graded Wiener-algebra methods. The norm given by the least common weighted...