相关论文: Bounded Hankel products on Fock-Sobolev spaces

The Product Conjecture for the homological Bieri-Neumann-Strebel-Renz invariants is proved over a field. Under certain hypotheses the Product Conjecture is shown to also hold over Z, even though D. Schuetz has recently shown that the…

Strong cosmic censorship conjecture has been one of the most important leap of faith in the context of general relativity, providing assurance in the deterministic nature of the associated field equations. Though it holds well for…

In this paper, we consider Hankel operators, with locally integrable symbols, densely defined on a family of Fock-type spaces whose weights are $C^3$-logarithmic growth functions with mild smoothness conditions. It is shown that a Hankel…

In this paper, we show that certain sums of generalized $m$-gonal numbers represent every positive integer if and only if they represent every positive integer up to an explicit bound $C_m$, verifying a conjecture of Sun for sufficiently…

We study convergent sequences of Baumslag-Solitar groups in the space of marked groups. We prove that BS(m,n) --> F_2 for |m|,|n| --> \infty and BS(1,n) --> Z \wr Z for |n| --> \infty. For m fixed, |m|>1, we show that the sequence…

For a compact set $A$ in $\mathbb{R}^n$ the Hausdorff distance from $A$ to $\text{conv}(A)$ is defined by \begin{equation*} d(A):=\sup_{a\in\text{conv}(A)}\inf_{x\in A}|x-a|, \end{equation*} where for $x=(x_1,\dots,x_n)\in\mathbb{R}^n$ we…

The F-conjecture gives a conjectural description of the ample cone of the Deligne-Mumford moduli space $\overline{M}_{g,n}$. We prove that the $S_n$-symmetric and the non-symmetric F-conjectures are equivalent. We also prove the Strong…

We prove some new instances of a conjecture of Bachoc, Couvreur and Z\'emor that generalizes Freiman's $3k-4$ Theorem to a multiplicative version in a function field setting. As a consequence we find that if $F$ is a rational function field…

We establish the volume conjecture for (m,2)-cables of the figure 8 knot, when m is odd. For (m,2)-cables of general knots where m is even, we show that the limit in the volume conjecture depends on the parity of the color (of the Kashaev…

Inspired by the quantitative $K$-theory, in this paper, we introduce the coarse Baum-Connes conjecture with filtered coefficients which generalizes the original conjecture. There are two advantages for the conjecture with filtered…

We propose a conjectural semiorthogonal decomposition for the derived category of the moduli space of stable rank 2 bundles with fixed determinant of odd degree, independently formulated by Narasimhan. We discuss some evidence for, and…

Using the notion of integral distance to analytic functions, we give a characterization of Schatten class Hankel operators acting on doubling Fock spaces on the complex plane and use it to show that for $f\in L^{\infty}$, if $H_{f}$ is…

We consider Fock spaces $F^{p,\ell}_{\alpha}$ of entire functions on ${\mathbb C}$ associated to the weights $e^{-\alpha |z|^{2\ell}}$, where $\alpha>0$ and $\ell$ is a positive integer. We compute explicitly the corresponding Bergman…

It has been conjectured by Prokhorov and Shokurov that the moduli part in the canonical bundle formula is effectively b-semiample. In this work we reduce this conjecture to the case where the base of the fibration has dimension one.…

The Mishchenko-Fomenko conjecture says that for each real or complex finite-dimensional Lie algebra $\goth g$ there exists a complete set of commuting polynomials on its dual space $\goth g^*$. In terms of the theory of integrable…

Several cases of Fock space duality occurring in the theory of many-body systems in general and nuclei in particular are discussed. All of them are special cases of a general duality theorem proved in mathematics by Howe in the 1970s.…

More than twenty-five years ago, Manickam, Mikl\'{o}s, and Singhi conjectured that for positive integers $n,k$ with $n \geq 4k$, every set of $n$ real numbers with nonnegative sum has at least $\binom{n-1}{k-1}$ $k$-element subsets whose…

The author introduces a conjecture about Makar-Limanov invariants of affine unique factorization domains over a field of characteristic zero. Then the author finds that the conjecture does not always hold when $\mathbbm{k}$ is not…

The Fuglede conjecture states that a set is spectral if and only if it tiles by translation. The conjecture was disproved by T. Tao for dimensions 5 and higher by giving a counterexample in $\mathbb{Z}_3^5$. We present a computer program…

We give a direct proof of a result due to Karasev (2008), Karasev-Matschke (2014) and Schnider-Sober\'on (2023). Given $m+1$ Borel probability measures on the space of affine hyperplanes in a real vector space $V$ of dimension $m+1$, there…