Related papers: Twisted Adiabatic Limit for Complex Structures
We consider the Hilbert-type operator defined by $$ H_{\omega}(f)(z)=\int_0^1 f(t)\left(\frac{1}{z}\int_0^z B^{\omega}_t(u)\,du\right)\,\omega(t)dt,$$ where $\{B^{\omega}_\zeta\}_{\zeta\in\mathbb{D}}$ are the reproducing kernels of the…
In this paper, we study the perturbative aspects of a twisted version of the two-dimensional $(0,2)$ heterotic sigma model on a holomorphic gauge bundle $\mathcal E$ over a complex, hermitian manifold $X$. We show that the model can be…
In this paper, we introduce the cohomology theory of $\mathcal{O}$-operators on Hom-associative algebras. This cohomology can also be viewed as the Hochschild cohomology of a certain Hom-associative algebra with coefficients in a suitable…
We introduce a notion of smooth fields of operators following the notion of smooth fields of Hilbert spaces recently defined by L. Lempert and R. Sz\H{o}oke arXiv:1004.4863(2) . Formally, if $\nabla$ is the connection of a smooth field of…
The ring $\text{Diff}_{\mathbf{h}}(n)$ of $\mathbf{h}$-deformed differential operators appears in the theory of reduction algebras. In this thesis, we construct the rings of generalized differential operators on the $\mathbf{h}$-deformed…
We introduce the notion of a twisted differential operator of given radius relative to an endomorphism $$\sigma$$ of an affinoid algebra A. We show that this notion is essentially independent of the choice of the endomorphism $$\sigma$$. As…
It is shown that an elliptic scattering operator $A$ on a compact manifold with boundary with coefficients in the bounded operators of a bundle of Banach spaces of class (HT) and Pisier's property $(\alpha)$ has maximal regularity (up to a…
Exact nonadiabatic quantum evolution preserves many geometric properties of the molecular Hilbert space. In a companion paper [S. Choi and J. Van\'{\i}\v{c}ek, 2019], we presented numerical integrators of arbitrary-order of accuracy that…
If $(\eta )=\{ \eta_n\} _{n=0}^\infty $ is a sequence of complex numbers, the Ces\`aro-type operator $\mathcal C_{(\eta )}$ is formally defined in the space of analytic funtions in the unit disc $\mathbb D$ as follows: If $f$ is an analytic…
The adiabatic theorem and "shortcuts to adiabaticity" for the adiabatic dynamics of time-dependent decoherence-free subspaces are explored in this paper. Starting from the definition of the dynamical stable decoherence-free subspaces, we…
The variance of a bounded linear operator $a$ on a Hilbert space $H$ at a unit vector $h$ is defined by $D_h(a)=\|ah\|^2-|<ah,h>|^2$. We show that two operators $a$ and $b$ have the same variance at all vectors $h\in H$ if and only if there…
A curvature inequality is established for contractive commuting tuples of operators in the Cowen-Douglas class of rank n. Properties of the extremal operators, that is, the operators which achieve equality, are investigated. Specifically, a…
We study the moments of $\overline{|\det(H-E)|^q}$ and the associated large deviations of $\log |\det(H-E)|$ where $H$ are random matrix operators involving Laplace operators and random potentials. This includes as a special case Hessians…
We introduce and study invariant differential operators acting on the space $\mathcal{H}(\Omega)$ of holomorphic functions on the complement ${\Omega=\{(z,w) \in \hat{\mathbb{C}}^2 \, : \, z\cdot w \not=1\}}$ of the "complexified unit…
In recent years, algebras and modules of differential operators have been extensively studied. Equivariant quantization and dequantization establish a tight link between invariant operators connecting modules of differential operators on…
Motivated by the discrete dipole approximation (DDA) for the scattering of electromagnetic waves by a dielectric obstacle that can be considered as a simple discretization of a Lippmann-Schwinger style volume integral equation for…
The main result of the paper is an extension of the Dirichlet problem from (closures of) bounded open domains U to arbitrary compact subsets X of the complex plane, i.e. the closure of the corresponding space of functions which are harmonic…
In a recent paper, Belishev and Sharafutdinov consider a compact Riemannian manifold $M$ with boundary $\partial M$. They define a generalized Dirichlet to Neumann (DN) operator $\Lambda$ on all forms on the boundary and they prove that the…
The basic framework for this article is the causal set approach to discrete quantum gravity (DQG). Let $Q_n$ be the collection of causal sets with cardinality not greater than $n$ and let $K_n$ be the standard Hilbert space of…
Let T be the singular integral operator with variable kernel defined by $Tf(x)= p.v. \int_{\mathbb{R}^{n}}K(x,x-y)f(y)\mathrm{d}y$ and $D^{\gamma}(0\leq\gamma\leq1)$ be the fractional differentiation operator, where…