Jul 2026· SIAM Journal on Mathematical Analysis· Vol 58, pp. 3898-3920· 0 citations· 25 references
Computer Science
Abstract
Abstract.
We prove that, among all subsets [Formula: see text] having circular symmetry and prescribed measure, the ball is the only maximizer of the sum of the first [Formula: see text] eigenvalues ([Formula: see text]) of the corresponding Toeplitz operator [Formula: see text] on the Fock space [Formula: see text]. As a byproduct, we prove that, again among circularly symmetric sets of prescribed measure, balls maximize any Schatten [Formula: see text]-norm of [Formula: see text] for [Formula: see text] (and minimize the corresponding quasinorm for [Formula: see text]), and that the second eigenvalue is maximized by a particular annulus. Moreover, we extend some of these results to general radial symbols in [Formula: see text] with [Formula: see text], characterizing those that maximize the sum of the first [Formula: see text] eigenvalues. We also show a symmetry breaking phenomenon for the second eigenvalue, when the assumption of circular symmetry is dropped.
We study a symmetry problem for the [Formula: see text]-polynomials of edge rings of bipartite graphs. Let [Formula: see text] be a bipartite graph and write [Formula: see text]. We prove that if [Formula: see text] is pseudo-Gorenstein and [Formula: see text], then [Formula: see text] is Gorenstein. Equivalently, unde...
Yuta Hatasa· Journal of Algebra and its A...· 0 citations
In this work, we study analytic deformations of a pencil [Formula: see text] where [Formula: see text] and [Formula: see text] are holomorphic functions defined in [Formula: see text], and [Formula: see text] are relatively prime integers. We consider analytic deformations given by integrable [Formula: see text]-forms...
B. Scárdua· International Journal of Mat...· 0 citations
This paper investigates the structural properties of the set of [Formula: see text]th roots of unity in a finite group [Formula: see text], defined as [Formula: see text]. We focus on two primary inquiries: the conditions under which these sets constitute subgroups and the validity of the unique order property, which a...
Boaz Cohen· Asian-European Journal of Ma...· 0 citations
Let [Formula: see text] be a reproducing kernel Hilbert space, fix [Formula: see text], and assume that its normalized kernel family contains pairs with inner product [Formula: see text]. We obtain upper bounds for the [Formula: see text]-Berezin radius in terms of the Berezin number and [Formula: see text], where [For...
Hamdullah Başaran, M. Gürdal, F. Kıttaneh et al.· International Journal of Mat...· 0 citations
Singular knots are smooth maps [Formula: see text] that have self-intersections or points at which the derivative vanishes. We describe an algebraic classification of their singularities, and study the topological properties of the corresponding stratification of the discriminant subset [Formula: see text] consisting o...
V. Vassiliev· Journal of knot theory and i...· 0 citations
Abstract.
In this paper, we investigate the perturbed Trudinger–Moser inequalities as follows: [Formula: see text] where [Formula: see text] and [Formula: see text] is a bounded domain in [Formula: see text]. Our results demonstrate that there exists a threshold [Formula: see text] such that [Formula: see text] is att...
Lu Chen, Rou Jiang, Guo-Zhen Lu et al.· SIAM Journal on Mathematical...· 1 citation
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