相关论文: The Hodge star operator on Schubert forms
We study the mapping property of the commutator of bilinear Hardy-Littlewood maximal operator in homogeneous Triebel-Lizorkin space. We also show that the commutator of bilinear Hardy-Littlewood maximal operator is a compact operator acting…
The isomonodromic tau function of the Fuchsian differential equations associated to Frobenius structures on Hurwitz spaces can be viewed as a section of a line bundle on the space of admissible covers. We study the asymptotic behavior of…
In a recent paper it was shown that if a Hamiltonian H has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT. The inner product with respect to…
We introduce a notion of ellipticity of complexes of linear pseudodifferential operators acting on sections of $A$-Hilbert bundles over smooth manifolds, $A$ being a $C^*$-algebra. We prove that the cohomology groups of an $A$-elliptic…
We make a progress towards describing the commutants of Toeplitz operators with harmonic symbols on the Bergman space over the unit disk. Our work greatly generalizes several partial results in the field.
In this article, we define discrete analogue of generalized Hardy spaces and its separable subspace on a homogenous rooted tree and study some of its properties such as completeness, inclusion relations with other spaces, separability,…
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the…
We develop potential theory for $m$-subharmonic functions with respect to a Hermitian metric on a Hermitian manifold. First, we show that the complex Hessian operator is well-defined for bounded functions in this class. This allows to…
We complete the classification of isometric cohomogeneity-one actions on all symmetric spaces of noncompact type up to orbit equivalence.
Let $G$ be a finite pseudoreflection group and $\Omega\subseteq \mathbb C^d$ be a bounded domain which is a $G$-space. We establish identities involving Toeplitz operators on the weighted Bergman spaces of $\Omega$ and $\Omega/G$ using…
In the finite-dimensional setting, every Hermitian-symmetric space of compact type is a coadjoint orbit of a finite-dimensional Lie group. It is natural to ask whether every infinite-dimensional Hermitian-symmetric space of compact type,…
We study super-braided Hopf algebras $\Lambda$ primitively generated by finite-dimensional right crossed (or Drinfeld-Radford-Yetter) modules $\Lambda^1$ over a Hopf algebra $A$ which are quotients of the augmentation ideal $A^+$ under…
The aim of this paper is to study when two composition operators on the Hilbert space of Dirichlet series with square summable coefficients belong to the same component or when their difference is compact. As a corollary we show that if a…
Let X = G/P be a cominuscule rational homogeneous variety. (Equivalently, X admits the structure of a compact Hermitian symmetric space.) I give a uniform description (that is, independent of type) of the irreducible components of the…
For an invertible (bounded) linear operator Q acting in a Hilbert space ${\cal H}$, we consider the consequences of the QT-symmetry of a non-Hermitian Hamiltonian $H:{\cal H}\to{\cal H}$ where T is the time-reversal operator. If H is…
An essentially unique homeomorphic solution to the Beltrami equation was found in the 1960s using the theory of Calder\'{o}n-Zygmund and singular integral operators in $L^p(\mathbb C)$. We will present an alternative method to solve the…
We study the algebra of differential operators on non-compact simply connected harmonic manifolds and provide sufficient conditions for them to have a radial fundamental solution and be surjective on the space of smooth function.…
In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are {\em homogeneous} with respect to the action of the M\"{o}bius group consisting of bi-holomorphic automorphisms of the unit…
Complex geometric properties of the orbits of a non-compact real form $G_0$ in a flag manifold $Z=G/Q$ of a complex semi-simple groups $G=G_0^\mathbb C$ are studied. Schubert varieties are used to construct a complex submanifold with…
We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum…