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861.
Siva R. Athreya Richard F. Bass Edwin A. Perkins 《Transactions of the American Mathematical Society》2005,357(12):5001-5029
We introduce a new method for proving the estimate
where solves the equation . The method can be applied to the Laplacian on . It also allows us to obtain similar estimates when we replace the Laplacian by an infinite-dimensional Ornstein-Uhlenbeck operator or other elliptic operators. These operators arise naturally in martingale problems arising from measure-valued branching diffusions and from stochastic partial differential equations.
where solves the equation . The method can be applied to the Laplacian on . It also allows us to obtain similar estimates when we replace the Laplacian by an infinite-dimensional Ornstein-Uhlenbeck operator or other elliptic operators. These operators arise naturally in martingale problems arising from measure-valued branching diffusions and from stochastic partial differential equations.
862.
Olivier Bourget 《Journal of Mathematical Analysis and Applications》2005,301(1):65-83
Consider the Floquet operator of a time independent quantum system, acting on a separable Hilbert space, periodically perturbed by a rank one kick: e−iH0Te−iκT|?〉〈?| where T is the period, κ the coupling constant, and H0 is a pure point self-adjoint operator, bounded from below. Under some hypotheses on the vector ?, cyclic w.r.t. H0 we prove the following:
- •
- If the gaps between the eigenvalues (λn) are such that λn+1−λn?Cn−γ for some γ∈]0,1[ and C>0, then the Floquet operator of the perturbed system is purely singular continuous T-a.e.
- •
- If H0 is the Hamiltonian of the one-dimensional rotator on L2(R/T0Z) and the ratio is irrational, then the Floquet operator is purely singular continuous as soon as κT≠0(2π).
863.
V. P. Karassiov 《Theoretical and Mathematical Physics》2005,145(3):1666-1677
We present theoretical foundations for the quantum tomography of polarization states of light fields as a method for measuring
their polarization density operator
, which characterizes only the polarization degrees of freedom of the radiation. We mainly attend to the method in which the
tomographic observables (the
“measurement instruments”) are polarizable in nature. We show that the quantum nature of this method can be adequately expressed
using the quasispectral tomographic decompositions of
in special operator bases, which are finite sums of partially orthogonal projection operators determining the probability
distributions of tomographic observables as the decomposition coefficients. We obtain the matrix versions of such “tomographic”
representations of
, in particular, by projecting them on semiclassical operator bases determining the polarization quasiprobability functions.
We briefly discuss the information aspects of the schemes considered in the paper.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 3, pp. 344–357, December, 2005. 相似文献
864.
865.
The minimal representation of O(p,q) (p+q: even) is realized on the Hilbert space of square integrable functions on the conical subvariety of Rp+q–2. This model presents a close resemblance of the Schrödinger model of the Segal–Shale–Weil representation of the metaplectic group. We shall give explicit integral formulas for the inversion together with the analytic continuation to a certain semigroup of O(p+2,C) of the minimal representation of O(p,2) by using Bessel functions.Mathematics Subject Classifications (2000) primary 22E30; secondary 22E46, 20M20, 43A80. 相似文献
866.
We prove existence and uniqueness results for non-linear elliptic equations with lower order terms, L1 data, and mixed boundary conditions that include as particular cases the Dirichlet and the Neumann problems.
Mathematics Subject Classification (2000) 35J25, 35D05, 35J70, 35J60 相似文献
867.
We show that for a positive linear operator acting in ℓ2 and defined from
anxn+1+bnxn+an-1xn-1