Related papers: Second Quantization and Evolution Operators in inf…
We study the Cauchy problem associated to parabolic systems of the form $D_t\boldsymbol{u}=\boldsymbol{\mathcal A}(t)\boldsymbol u$ in $C_b(\mathbb{R}^d;\mathbb{R}^m)$, the space of continuous and bounded functions…
In this paper, we consider non-autonomous Ornstein-Uhlenbeck operators in smooth exterior domains $\Omega\subset \R^d$ subject to Dirichlet boundary conditions. Under suitable assumptions on the coefficients, the solution of the…
We provide a framework to determine the upper bound to the complexity of a computing a given observable with respect to a Hamiltonian. By considering the Heisenberg evolution of the observable, we show that each Hamiltonian defines an…
We present a simple and self-contained approach to establish the unique continuation property for some classical evolution equations of second order in a cylindrical domain. We namely discuss this property for wave, parabolic and…
We study analytic models of operators of class $C_{\cdot 0}$ with natural positivity assumptions. In particular, we prove that for an $m$-hypercontraction $T \in C_{\cdot 0}$ on a Hilbert space $\mathcal{H}$, there exists a Hilbert space…
Let $X$ be a separable Banach space and let $Q:X^*\rightarrow X$ be a linear, bounded, non-negative and symmetric operator and let $A:D(A)\subseteq X\rightarrow X$ be the infinitesimal generator of a strongly continuous semigroup of…
This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of the continuous time trajectories to sequences generated by…
The classical $L^2$ estimate for the $\overline{\partial}$ operators is a basic tool in complex analysis of several variables. Naturally, it is expected to extend this estimate to infinite dimensional complex analysis, but this is a…
In this paper, building on a previous analysis [1] of exact diagonalization of the space-discretized evolution operator for the study of properties of non-relativistic quantum systems, we present a substantial improvement to this method. We…
We construct quantum evolution operators on the space of states, that is represented by the vertices of the n-dimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2,Z(2^n)). By construction this…
Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…
In this paper, we consider the transport properties of the class of limit-periodic continuum Schr\"odinger operators whose potentials are approximated exponentially quickly by a sequence of periodic functions. For such an operator $H$, and…
Boundedness and compactness properties of multiplication operators on quantum (non-commutative) function spaces are investigated. For endomorphic multiplication operators these properties can be characterized in the setting of quantum…
In this paper we revisit the mild-solution approach to second-order semi-linear PDEs of Hamilton-Jacobi type in infinite-dimensional spaces. We show that a well-known result on existence of mild solutions in Hilbert spaces can be easily…
In a separable Hilbert space $X$, we study the controlled evolution equation \begin{equation*} u'(t)+Au(t)+p(t)Bu(t)=0, \end{equation*} where $A\geq-\sigma I$ ($\sigma\geq0$) is a self-adjoint linear operator, $B$ is a bounded linear…
Selfadjoint and maximal dissipative extensions of a non-densely defined symmetric operator $S$ in an infinite-dimensional separable Hilbert space are considered and their compressions on the subspace ${\rm \overline{dom}\,} S$ are studied.…
We prove under certain assumptions that there exists a solution of the Schrodinger or the Heisenberg equation of motion generated by a linear operator H acting in some complex Hilbert space H, which may be unbounded, not symmetric, or not…
We provide a summary of the continuity properties of the boundary integral operator corresponding to the double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator…
This paper studies the \(k^{th}-\)order slant Toeplitz and slant little Hankel operators on the weighted Bergman space \(\mathcal{A}_\alpha^2(\mathbb{D})\). These operators are constructed using a slant shift operator \(W_k\) composed with…
Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…