This paper is concerned with the well-posedness analysis of the Hartree-Fock system modeling the time evolution of a quantum system comprised of fermions. We consider quantum states with finite mass and finite kinetic energy, and the self-consistent potential is the unbounded Coulomb interaction. This model is first formulated as a semi-linear evolution problem for the one-particle density matr...

Let D be a Dirac type operator on a compact manifold M and let Σ be a Lipschitz submanifold of codimension one partitioningM into two Lipschitz domains Ω±. Also, let Hp±(Σ, D) be the traces on Σ of the (Lpstyle) Hardy spaces associated with D in Ω±. Then (Hp−(Σ, D),Hp+(Σ, D)) is a Fredholm pair of subspaces for Lp(Σ) (in Kato’s sense) whose index is the same as the index of the Dirac operator D...

The spectral shift function for a trace class perturbation of a self-adjoint (unitary) operator plays a very important role in perturbation theory. It was introduced in a special case by I.M. Lifshitz [L] and in the general case by M.G. Krein [Kr1]. He showed that for a pair of self-adjoint (not necessarily bounded) operators A and B satisfying B −A ∈ S1 there exists a unique function ξ ∈ L 1(R...

probability of occurrences. However, in the current paper, we discuss the issue of identifying a target strategy exactly from trace data. Learning criterion used in this paper is the identi cation in the limit proposed by Gold. Further, we use the tree pattern language to represent preconditions of operators, and propose a class of strategies, called decision list strategies. One of the interes...

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...

A general quantum history theory can be characterised by the space of histories and by the space of decoherence functionals. In this note we consider the situation where the space of histories is given by the lattice of projection operators on an infinite dimensional Hilbert space H. We study operator representations for decoherence functionals on this space of histories. We first give necessar...

In this article the operator trace function Λr,s(A)[K,M]:=tr(K⁎ArMArK)s is introduced and its convexity concavity properties are investigated. This has a direct connection to several well-studied functions that appear in quantum information theory, particular when studying data processing inequalities of various relative entropies. paper interplay between Λr,s well-known Γp,s Ψp,q,s used study ...