Mathematische Annalen最新文献

It is shown using Schur complement techniques that on dimensional Hilbert spaces, a non-negative operator valued trigonometric polynomial in two variables with degree ((d_1,d_2)) can be written as a sum of hermitian squares of at most (2d_2) analytic polynomials.

Given a self-adjoint operator T on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set ({mathcal {D}}(T)) of all possible diagonals of T. For operators T with at least two points in their essential spectrum (sigma _{ess}(T)), we give a complete characterization of ({mathcal {D}}(T)) for the class of self-adjoint operators sharing the same spectral measure as T with a possible exception of multiplicities of eigenvalues at the extreme points of (sigma _{ess}(T)). We also give a more precise description of ({mathcal {D}}(T)) for a fixed self-adjoint operator T, albeit modulo the kernel problem for special classes of operators. These classes consist of operators T for which an extreme point of the essential spectrum (sigma _{ess}(T)) is also an extreme point of the spectrum (sigma (T)). Our results generalize a characterization of diagonals of orthogonal projections by Kadison [38, 39], Blaschke-type results of Müller and Tomilov [51] and Loreaux and Weiss [48], and a characterization of diagonals of operators with finite spectrum by the authors [15].

This is a sequel to our previous articles (Kwan in Algebra Number Theory. arXiv:2112.08568v4; Kwan in Spectral moment formulae for (GL(3)times GL(2)) L-functions II: Eisenstein case, 2023. arXiv:2310.09419). In this work, we apply recent techniques that fall under the banner of ‘Period Reciprocity’ to study moments of (GL(3)times GL(2)) L-functions in the non-archimedean aspects, with a view towards the ‘Twisted Moment Conjectures’ formulated by CFKRS.

We show that the decision problem of recognising whether a triangulated 3-manifold admits a Seifert fibered structure with non-empty boundary is in NP. We also show that the problem of deciding whether a given triangulated Seifert fibered space with non-empty boundary admits certain Seifert data is in ({{{textbf {NP}}}{}}cap text {co-}{} {textbf {NP}}). We do this by proving that in any triangulation of a Seifert fibered space with boundary there is both a fundamental horizontal surface of small degree and a complete collection of normal vertical annuli whose total weight is bounded by an exponential in the square of the triangulation size.

The main contribution of this paper is to provide a complete proof of the global weak entropy solution existence of the Cauchy problem for the Euler equations of one-dimensional compressible fluid flow and to correct the mistakes in the paper “Global weak solutions of the one-dimensional hydrodynamic model for semiconductors” (Math. Mod. Meth. Appl. Sci., 6(1993), 759–788). Our technique is the method of the artificial viscosity coupled with the theory of compensated compactness, where four families of Lax entropy-entropy flux pair are constructed by means of the classical Fuchsian equation.

In this paper, we show that for each (kin {mathbb {Z}}^+, p>4), there exists a solution operator ({mathcal {T}}_k) to the (bar{partial }) problem on the Hartogs triangle that maintains the same (W^{k, p}) regularity as that of the data. According to a Kerzman-type example, this operator provides solutions with the optimal Sobolev regularity.

Although exotic blow-ups of the projective plane at n points have been constructed for every (n ge 2), the only examples known by means of rational blowdowns satisfy (n ge 5). It has been an intriguing problem whether it is possible to decrease n. In this paper, we construct the first exotic ({mathbb {C}}{mathbb {P}}^2 # 4 overline{{mathbb {C}}{mathbb {P}}^2}) with this technique. We also construct exotic (3{mathbb {C}}{mathbb {P}}^2 # b^- overline{{mathbb {C}}{mathbb {P}}^2}) for (b^-=9,8,7). All of them are minimal and symplectic, as they are produced from projective surfaces W with Wahl singularities and (K_W) big and nef. In more generality, we elaborate on the problem of finding exotic

from these Kollár–Shepherd-Barron–Alexeev surfaces W, obtaining explicit geometric obstructions on the corresponding configurations of rational curves.

Let X be a smooth Fano variety. We attach a bi-graded associative algebra (textrm{HS}(mathcal {K}u(X))=bigoplus _{i,jin mathbb {Z}} textrm{Hom}(textrm{Id},S_{mathcal {K}u(X)}^{i}[j])) to the Kuznetsov component (mathcal {K}u(X)) whenever it is defined. Then we construct a natural sub-algebra of (textrm{HS}(mathcal {K}u(X))) when X is a Fano hypersurface and establish its relation with Jacobian ring (textrm{Jac}(X)). As an application, we prove a categorical Torelli theorem for Fano hypersurface (Xsubset mathbb {P}^n(nge 2)) of degree d if (textrm{gcd}((n+1),d)=1.) In addition, we give a new proof of the main theorem [15, Theorem 1.2] using a similar idea.

We show that distinct primitive L-functions can achieve extreme values simultaneously on the critical line. Our proof uses a modification of the resonance method and can be applied to establish simultaneous extreme central values of L-functions in families.

We consider the varifold associated to the Allen–Cahn phase transition problem in ({mathbb {R}}^{n+1})(or (n+1)-dimensional Riemannian manifolds with bounded curvature) with integral (L^{q_0}) bounds on the Allen–Cahn mean curvature (first variation of the Allen–Cahn energy) in this paper. It is shown here that there is an equidistribution of energy between the Dirichlet and Potential energy in the phase field limit and that the associated varifold to the total energy converges to an integer rectifiable varifold with mean curvature in (L^{q_0}, q_0 > n). The latter is a diffused version of Allard’s convergence theorem for integer rectifiable varifolds.