Related papers: Counterexample to the Laptev--Safronov conjecture
We study periodic approximations of aperiodic Schr\"odinger operators on lattices in Lie groups with dilation structure. The potentials arise through symbolic substitution systems that have been recently introduced in this setting. We…
Let $(\lambda_k)$ be a strictly increasing sequence of positive numbers such that $\sum_{k=1}^{\infty} \frac{1}{\lambda_k} < \infty.$ Let $f $ be a bounded smooth function and denote by $u= u^f$ the bounded classical solution to $u(x) -…
In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.
We verify Katzarkov-Kontsevich-Pantev conjecture for Landau-Ginzburg models of smooth Fano threefolds.
We construct an entire function $f$ with only three singular values whose order of growth can change under a quasiconformal equivalence. This is a counterexample to the Order Conjecture in the Speiser class ${\mathcal S}$ of entire…
We discuss the question of Ralf-Dieter Schindler whether for infinite time Turing machines P^f = NP^f can be true for any function f from the reals into omega_1. We show that ``almost everywhere'' the answer is negative.
In this paper, we prove a conjecture of Schnell in the surface case.
New estimates for eigenvalues of non-self-adjoint multi-dimensional Schr\"{o}dinger operators are obtained in terms of $L_{p}$-norms of the potentials. The results extend and improve those obtained previously. In particular, diverse…
We study the failure of the Lipman-Zariski conjecture in positive characteristic. For rational double points, the conjecture holds true except for a short finite list of exceptions. For log canonical surface singularities, the conjecture…
Akemann and Weaver (2014) have shown a remarkable extension of Weaver's $KS_r$ Conjecture (2004) in the form of approximate Lyapunov's theorem. This was made possible thanks to the breakthrough solution of the Kadison-Singer problem by…
We consider a family of non-local and non-convex functionals, and we prove that their Gamma-liminf is bounded from below by a positive multiple of the Sobolev norm or the total variation. As a by-product, we answer some open questions…
Under Wigdersons' framework and by sorting out the technical points in the recent works of Tang (J. Fourier Anal. Appl. 31 (2025)) and Dias-Luef-Prata (J. Math. Pures Appl. (9) 198 (2025)), we prove an abstract uncertainty principle for…
The paper is a reply to the arguments adduced by the authors of Ref. [arXiv:1204.4142] against the results obtained by the author in Refs. [6,7]. It is shown that these arguments are based on the erroneous approach made in Ref.…
In this article, we study multivariate generalizations of the Matsaev's conjecture in commutative and non-commutative $L^p$-spaces.We prove that the multivariate analogue of Matsaev's conjecture is eventually false for all $1<p<\infty.$ We…
Nous pr\'esentons un r\'esultat d'absence de spectre absolument continu dans un intervalle de $\R$ pour un op\'erateur de Schr\"odinger al\'eatoire continu et \`a valeurs matricielles agissant sur $L^2(\R)\otimes \C^N$ pour $N\geq 1$…
We obtain some results related to Romanoff's theorem.
We prove dispersive estimates for the low frequency part of the Schrodinger group for a large class of potentials in dimensions greater or equal to four. As a consequence, we extend the result of Journe, Sofer and Sogge to a larger class of…
We prove that the classical Efron--Stein inequality holds for independent exchangeable pairs \((X_i,Y_i)\). The same inequality fails for independent identically distributed pairs; a simple trigonometric counterexample shows that the…
It is shown that the 1-dimensional lattice Schrodinger operator with potential given by a non-zero multiple of the Moebius function has positive Lyapounov exponent. In view of the classical theory of random Schrodinger operators, this may…
A recent paper (arXiv:1404.5619) claimed the presence of a loophole in the current-algebra proof of Goldstone Theorem. The enforcing of manifest covariance would lead to contradictory results also in scalar theory. We show that the argument…