Mathematische Annalen最新文献

This note aim to provide a deeper insight on article dealing with an inverse problem for biharmonic operator with second order perturbation. More precisely, we are referring to the paper An inverse problem on determining second order symmetric tensor for perturbed biharmonic operator by Bhattacharyya and Ghosh An inverse problem on determining second order symmetric tensor for perturbed biharmonic operator, Math Ann (2021). Unfortunately, the paper contains some incorrect part. Indeed, a gap in the proof of the crucial proposition appears, whereas Proposition 3.6 in Bhattacharyya and Ghosh (Math Ann, 2021) is true only in a very specific case.

In this paper we consider a class of evolution operators with coefficients depending on time and space variables ((t,x) in {mathbb {T}}times {mathbb {R}}^n), where ({mathbb {T}}) is the one-dimensional torus, and prove necessary and sufficient conditions for their global solvability in (time-periodic) Gelfand–Shilov spaces. The argument of the proof is based on a characterization of these spaces in terms of the eigenfunction expansions given by a fixed self-adjoint, globally elliptic differential operator on ({mathbb {R}}^n).

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.