Titlebook: Lectures on the Mathematics of Quantum Mechanics II: Selected Topics; Gianfausto Dell‘Antonio Book 2016 Atlantis Press and the author(s) 2

使坚硬

,Lecture 8: Ornstein–Uhlenbeck Process. Markov Structure. Semigroup Property. Paths Over Function SpThe structures we have analyzed so far describe random processes in the time interval [0, .] with . arbitrary but finite. One can equivalently consider processes in the time interval ..

战役

,Lecture 9: Modular Operator. Tomita–Takesaki Theory Non-commutative Integration,We review in this Lecture some basic elements of the . and its connections with the theory of Tomita–Takesaki which we treated very briefly in Volume I of these Lecture Notes.

远足

Morose

青石板

Lecture 12: The Method of Enss. Propagation Estimates. Mourre Method. Kato Smoothness, Elements of In this lecture we give more details of an alternative approach to quantum scattering theory, initiated by V. Enss, This approach is based on . of the behavior for . of the solutions of Schroedinger’s equation for initial data in the subspace of absolute continuity for the hamiltonian ..

乳汁

Lecture 14: Positivity Preserving Maps. Markov Semigropus. Contractive Dirichlet Forms,In Volume I we have remarked that in order that the operator . be self-adjoint the conditions on the positive part . of . are much weaker than the conditions on its negative part. In particular it not required that . be small with respect to the laplacian.

Veneer

Lecture 15: Hypercontractivity. Logarithmic Sobolev Inequalities. Harmonic Group,We ended the previous Lecture with an analysis of conditions under which the semigroup . has suitable regularizing properties.

TIGER

Bridle

Choreography

Lectures on the Mathematics of Quantum Mechanics II: Selected Topics978-94-6239-115-4Series ISSN 2211-8055 Series E-ISSN 2211-8063