Related papers: Commutators of Hilbert transforms along monomial c…

Let $H$ be an infinite-dimensional complex Hilbert space and let ${\mathcal G}_{\infty}(H)$ be the set of all closed subspaces of $H$ whose dimension and codimension both are infinite. We investigate (not necessarily surjective)…

Motivated by the theory of weighted shifts on directed trees and its multivariable counterpart, we address the question of identifying commutant and reflexivity of the multiplication $d$-tuple $\mathscr M_z$ on a reproducing kernel Hilbert…

We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including $L^p$-$L^q$, $L^p$-$BMO$ and $L^p$-Lipschitz estimates. The kernels of such operators satisfy…

The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. For compact topologies, the two main effects on the CMB are: (1) the…

We determine the homeomorphism type of the space of smooth complete nonnegatively curved metrics on surfaces of positive Euler characteristic equipped with the topology of $C^\gamma$ uniform convergence on compact sets, when $\gamma$ is…

We study the interplay between the recently defined concept of minimum homotopy area and the classical topic of self-overlapping curves. The latter are plane curves which are the image of the boundary of an immersed disk. Our first…

We focus on combinatorial aspects of the Hilbert series of the cohomology ring of the moduli space of stable pointed curves of genus zero. We show its graded Hilbert series satisfies an integral operator identity. This is used to give…

Let T be a C_{\cdot 0}-contraction on a Hilbert space H and S be a non-trivial closed subspace of H. We prove that S is a T-invariant subspace of H if and only if there exists a Hilbert space D and a partially isometric operator \Pi :…

Semi-cosimplicial objects in the category of Hilbert spaces with isometries which are motivated by non-commutative probability theory, in particular by the distributional symmetry of spreadability, are introduced and systematically…

Scale invariance provides a principled reason for the physical importance of Hilbert space, the Virasoro algebra, the string mode expansion, canonical commutators and Schroedinger evolution of states, independent of the assumptions of…

In this paper, some boundedness for commutators of fractional integrals are obtained on Herz-Morrey spaces with variable exponent applying some properties of varible exponent and $\BMO$ function.

Let $\widetilde{X}$ be a locally finite complete Gromov hyperbolic metric graph with the geometric boundary consisting of infinitely many points. Suppose that there is a discrete subgroup of the isometry group $Iso(\widetilde{X})$ acting…

In quantum mechanics (formulated, say, in Schr\"{o}dinger picture) only the knowledge of a complete set of observables $\Lambda_j$ enables us to declare the related physical inner product (i.e., the Hilbert-space metric $\Theta$ such that…

We study $L^p(\mu)$ estimates for the commutator $[H,b]$, where the operator $H$ is a dyadic model of the classical Hilbert transform introduced in \cite{arXiv:2012.10201,arXiv:2212.00090} and is adapted to a non-doubling Borel measure…

Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…

We give here the Hopf algebra structure describing the noncommutative renormalization of a recently introduced translation-invariant model on Moyal space. We define Hochschild one-cocyles $B_+^\gamma$ which allows us to write down the…

In this paper, we use the Ap\'ery table of the numerical semigroup associated to an affine monomial curve in order to characterize arithmetic properties and invariants of its tangent cone. In particular, we precise the shape of the Ap\'ery…

We prove that the operator norm on weighted Lebesgue space L2(w) of the commutators of the Hilbert, Riesz and Beurling transforms with a BMO function b depends quadratically on the A2-characteristic of the weight, as opposed to the linear…

Let $b$ be a symmetric or alternating bilinear form on a finite-dimensional vector space $V$. When the characteristic of the underlying field is not $2$, we determine the greatest dimension for a linear subspace of nilpotent $b$-symmetric…