Related papers: Outgoing monotone geodesics of standard subspaces

We construct natural operators connecting the cohomology of the moduli spaces of stable Higgs bundles with different ranks and genera which, after numerical specialization, recover the topological mirror symmetry conjecture of…

Manifest gauge-invariance requires that observable states in the standard-model are described by composite operators, which involve additional Higgs contributions beyond perturbation theory. This field-theoretical effect has been confirmed…

We show that the strong asymptotic class of Weil-Petersson (WP) geodesics with narrow end invariant and bounded annular coefficients is determined by the forward ending lamination. This generalizes the Recurrent Ending Lamination Theorem of…

We study the orthogonality of the generalized eigenspaces of an Ornstein--Uhlenbeck operator $\mathcal L$ in $\mathbb{R}^N$, with drift given by a real matrix $B$ whose eigenvalues have negative real parts. If $B$ has only one eigenvalue,…

We describe the category of regular holonomic modules over the ring D[[h]] of linear differential operators with a formal parameter h. In particular, we establish the Riemann-Hilbert correspondence and discuss the additional t-structure…

Let K be a finite field. Let X* be a subset of the affine space Kn, which is parameterized by odd cycles. In this paper we give an explicit Gr\"obner basis for the vanishing ideal, I(X*), of X*. We give an explicit formula for the…

Let M be either a simply connected pseudo-Riemannian space of constant curvature or a rank one Riemannian symmetric space (other than the octonion hyperbolic plane), and consider the space L(M) of oriented geodesics of M. The space L(M) is…

In this paper, a decomposition theorem for (covariant) unitary group representations on Kaplansky-Hilbert modules over Stone algebras is established, which generalizes the well-known Hilbert space case (where it coincides with the…

Standard subspaces are closed real subspaces of a complex Hilbert space that appear naturally in Tomita-Takesaki modular theory and its applications to quantum field theory. In this article, inclusions of standard subspaces are studied…

In analogy with the study of Pollicott-Ruelle resonances on negatively curved manifolds, we define anisotropic Sobolev spaces that are well-adapted to the analysis of the geodesic vector field associated with any translation invariant…

A $7$-tuple of commuting bounded operators $\mathbf{T} = (T_1, \dots, T_7)$ defined on a Hilbert space $\mathcal{H}$ is said to be a \textit{$\Gamma_{E(3; 3; 1, 1, 1)}$-contraction} if $\Gamma_{E(3; 3; 1, 1, 1)}$ is a spectral set for…

We consider linear operators defined on a subspace of a complex Banach space into its topological antidual acting positively in a natural sense. The goal of this paper is to investigate of this kind of operators. The main theorem is a…

The Bender-Dunne basis operators, $\mathsf{T}_{-m,n}=2^{-n}\sum_{k=0}^n {n \choose k} \mathsf{q}^k \mathsf{p}^{-m} \mathsf{q}^{n-k}$ where $\mathsf{q}$ and $\mathsf{p}$ are the position and momentum operators respectively, are formal…

We introduce new techniques allowing one to construct diagonals of bounded Hilbert space operators and operator tuples under "Blaschke-type" assumptions. This provides a new framework for a number of results in the literature and…

Suppose that S is a left amenable semitopological semigroup. We prove that if ${T_{t}: t \in S}$ is a uniformly k-Lipschitzian semigroup on a bounded closed and convex subset C of a Hilbert space and $k<\sqrt{2}$, then the set of fixed…

We study Weil-Petersson (WP) geodesics with narrow end invariant and develop techniques to control length-functions and twist parameters along them and prescribe their itinerary in the moduli space of Riemann surfaces. This class of…

Given an idempotent operator $E$ in a complex Hilbert space ${\mathcal H}$, one can associate to it two orthogonal projections: - The polar decomposition $2E-1=(2P-1)|2E-1|$ provides an orthogonal projection $P$. That the unitary part in…

The winding of a closed oriented geodesic around the cusp of the modular orbifold is computed by the Rademacher symbol, a classical function from the theory of modular forms. In this article, we introduce a new construction of winding…

We study exactness of groups and establish a characterization of exact groups in terms of the existence of a continuous linear operator, called an invariant expectation, whose properties make it a weak counterpart of an invariant mean on a…

Based on the work done in \cite{BV-Tind,DMS} in the o-minimal and geometric settings, we study expansions of models of a supersimple theory with a new predicate distiguishing a set of forking-independent elements that is dense inside a…