On a class of closed cocycles for algebras of non-formal, possibly unbounded, pseudodifferential operators

Schwinger Terms and Cohomology of Pseudodifferential Operators

We study the cohomology of the Schwinger term arising in second quantization of the class of observables belonging to the restricted general linear algebra. We prove that, for all pseudodifferential operators in 3+1 dimensions of this type, the Schwinger term is equivalent to the ``twisted'' Radul cocycle, a modified version of the Radul cocycle arising in non-commutative differential geometry. In the process we also show how the ordinary Radul cocycle for any pair of pseudodifferential operators in any dimension can be written as the phase space integral of the star commutator of their symbol…

多重算子积分、伪微分演算与渐近展开

Multiple operator integrals, pseudodifferential calculus, and asymptotic expansions

本文利用伪微分演算将多重算子积分推广至无界算子，为非交换几何提供自然语言，并给出谱作用的微扰展开及迹的渐近展开。

Norm Estimates for $τ$-Pseudodifferential Operators in Wiener Amalgam and Modulation Spaces

We study continuity properties on modulation spaces for $τ$-pseudodifferential operators with symbols $a$ in Wiener amalgam spaces. We obtain boundedness results for $τ\in (0,1)$ whereas, in the end-points $τ=0$ and $τ=1$, the corresponding operators are in general unbounded. Furthermore, for $τ\in (0,1)$, we exhibit a function of $τ$ which is an upper bound for the operator norm. The continuity properties of $τ$-pseudodifferential operators, for any $τ\in [0,1]$, with symbols $a$ in modulation spaces are well known. Here we find an upper bound for the operator norm which does not depend on th…

熵与抛物线伪微分算子的极小风险

Entropy and Minimax Risk of Hypoelliptic Pseudodifferential Operators

本文研究了广义紧致伪微分算子的熵和极小风险，结合Weyl型渐进行为与谱量、熵和极小风险的关系，推导出符号直接决定的渐近公式，并扩展了Pinsker定理至无界域的Sobolev空间。

Quantum stochastic cocycles and completely bounded semigroups on operator spaces II

Quantum stochastic cocycles provide a basic model for time-homogeneous Markovian evolutions in a quantum setting, and a direct counterpart in continuous time to quantum random walks, in both the Schrodinger and Heisenberg pictures. This paper is a sequel to one in which correspondences were established between classes of quantum stochastic cocycle on an operator space or C*-algebra, and classes of Schur-action `global' semigroup on associated matrix spaces over the operator space. In this paper we investigate the stochastic generation of cocycles via the generation of their corresponding globa…

An algebraic construction of quantum flows with unbounded generators

It is shown how to construct *-homomorphic quantum stochastic Feller cocycles for certain unbounded generators, and so obtain dilations of strongly continuous quantum dynamical semigroups on C* algebras; this generalises the construction of a classical Feller process and semigroup from a given generator. The construction is possible provided the generator satisfies an invariance property for some dense subalgebra A_0 of the C* algebra A and obeys the necessary structure relations; the iterates of the generator, when applied to a generating set for A_0, must satisfy a growth condition. Furtherm…