Journal of the London Mathematical Society-Second Series最新文献

We prove that many relatively hyperbolic groups obtained by relative strict hyperbolization admit a cocompact action on a $��CAT�\left(�0�\right)�$ cubical complex. Under suitable assumptions on the peripheral subgroups, these groups are residually finite and even virtually special. We include some applications to the theory of manifolds, such as the construction of new non-positively curved Riemannian manifolds with residually finite fundamental group, and the existence of non-triangulable aspherical manifolds with virtually special fundamental group.

Hardy's uncertainty principle is a classical result in harmonic analysis, stating that a function in $��L^2��\left(�R^d�\right)��$ and its Fourier transform cannot both decay arbitrarily fast at infinity. In this paper, we extend this principle to the propagators of Schrödinger equations with quadratic Hamiltonians, known in the literature as metaplectic operators. These operators generalize the Fourier transform and have captured significant attention in recent years due to their wide-ranging applications in time-frequency analysis, quantum harmonic analysis, signal processing, and various other fields. However, the involved structure of these operators requires careful analysis, and most results obtained so far concern special propagators that can basically be reduced to rescaled Fourier transforms. The main contributions of this work are threefold: (1) we extend Hardy's uncertainty principle, covering all propagators of Schrödinger equations with quadratic Hamiltonians, (2) we provide concrete examples, such as fractional Fourier transforms, which arise when considering anisotropic harmonic oscillators, (3) we suggest Gaussian decay conditions in certain directions only, which are related to the geometry of the corresponding Hamiltonian flow.

We establish regularity conditions for $�L_p$-boundedness of Fourier multipliers on the group von Neumann algebras of higher rank simple Lie groups. This provides a natural Hörmander–Mikhlin (HM) criterion in terms of Lie derivatives of the symbol and a metric given by the adjoint representation. In line with Lafforgue/de la Salle's rigidity theorem, our condition imposes certain decay of the symbol at infinity. It refines and vastly generalizes a recent result by Parcet, Ricard, and de la Salle for $��S�L_n��\left(�R�\right)��$. Our approach is partly based on a sharp local HM theorem for arbitrary Lie groups, which follows in turn from recent estimates by the authors on singular non-Toeplitz Schur multipliers. We generalize the latter to arbitrary locally compact groups and refine the cocycle-based approach to Fourier multipliers in group algebras by Junge, Mei, and Parcet. A few related open problems are also discussed.

We provide partial solutions to two problems posed by Shehtman concerning the modal logic of the Čech–Stone compactification of an ordinal space. We use the Continuum Hypothesis to give a finite axiomatization of the modal logic of $��\beta �\left(�{\omega }^2�\right)�$, thus resolving Shehtman's first problem for $��n�=�2�$. We also characterize modal logics arising from the Čech–Stone compactification of an ordinal $�\gamma$ provided the Cantor normal form of $�\gamma$ satisfies an additional condition. This gives a partial solution of Shehtman's second problem.

We introduce the notion of a twisted rational zero of a nondegenerate linear recurrence sequence (LRS). We show that any nondegenerate LRS has only finitely many such twisted rational zeros. In the particular case of the Tribonacci sequence, we show that $��1�/�3�$ and $��-�5�/�3�$ are the only twisted rational zeros that are not integral zeros.

We give a presentation of the torus-equivariant (small) quantum $�K$-theory ring of flag manifolds of type $�A$, as the quotient of a polynomial ring by an explicit ideal. This result is the torus-equivariant version of our previous one, which gives a presentation of the nonequivariant quantum $�K$-theory ring of flag manifolds of type $�A$. However, the method of proof for the torus-equivariant one is entirely different from that for the nonequivariant one; our proof is based on the result in the $��Q�=�0�$ limit, and uses Nakayama-type arguments to upgrade it to the quantum situation. Also, in contrast to the nonequivariant case in which we used the Chevalley formula, we make use of the inverse Chevalley formula for the torus-equivariant $�K$-group of semi-infinite flag manifolds to obtain relations that yield our presentation.

We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully noncentral, that is, its image in every quotient is noncentral. For a unital algebra over a field of characteristic $��\ne �2�$ where every additive commutator is a sum of square-zero elements, we show that a fully noncentral subspace is a Lie ideal if and only if it is invariant under all inner automorphisms. This applies in particular to zero-product balanced algebras.