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1.
We show that suitable upper estimates of the heat kernel are sufficient to imply the L
p
boundedness of several families of operators associated with the Schr?dinger group in various situations. This generalizes
results by Sj?strand and others in the Euclidean case, and by Alexopoulos in the case of Lie groups and Riemannian manifolds.
RID="*"
ID="*"Research partially supported by the European Commission (European TMR Network "Harmonic Analysis" 1998-2001, Contract
ERBFMRX-CT97-0159). 相似文献
2.
The diamagnetic inequality is established for the Schrödinger operator H(d)0 in L2
d=2,3, describing a particle moving in a magnetic field generated by finitely or infinitely many Aharonov-Bohm solenoids located at the points of a discrete set in
e.g., a lattice. This fact is used to prove the Lieb-Thirring inequality as well as CLR-type eigenvalue estimates for the perturbed Schrödinger operator H(d)0–V, using new Hardy type inequalities. Large coupling constant eigenvalue asymptotic formulas for the perturbed operators are also proved.Communicated by Bernard Helffersubmitted 02/12/03, accepted 12/03/04 相似文献
3.
Gabriela Ionita Petre Ionita Victor EM. Sahini Constantin Luca 《Journal of inclusion phenomena and macrocyclic chemistry》2001,39(3-4):269-271
The kinetics of oxidation of amino acids (Arg, His, Lys, Phe, Thr and Tyr), a dipeptide (Gly-His), and BSA (bovine serum albumin) by two persistent water soluble free radicals of the hydrazyl type has been studied.The rate decreases in the order Arg>Lys>Tyr>Thr>HisBSAPheGly-His with bothfree radicals. Addition to the reaction mixture of - and -cyclodextrin decreases the oxidation rate, probably due to amino acidencapsulation in the cyclodextrin cavity. -Cyclodextrin protects more efficiently against oxidation than -cyclodextrin. 相似文献
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We have used a variety of microscopic techniques to reveal the structure and motion of flux line arrangements, when the flux
lines in low T
c type II superconductors are caused to move by a transport current. Using small-angle neutron scattering by the flux line
lattice (FLL), we are able to demonstrate directly the alignment by motion of the nearest-neighbor FLL direction. This tends
to be parallel to the direction of flux line motion, as had been suspected from two-dimensional simulations. We also see the
destruction of the ordered FLL by plastic flow and the bending of flux lines. Another technique that our collaboration has
employed is the direct measurement of flux line motion, using the ultra-high-resolution spectroscopy of the neutron spin-echo
technique to observe the energy change of neutrons diffracted by moving flux lines. The muon spin rotation (μSR) technique gives the distribution of values of magnetic field within the FLL. We have recently succeeded in performing
μSR measurements while the FLL is moving. Such measurements give complementary information about the local speed and orientation
of the FLL motion. We conclude by discussing the possible application of this technique to thin film superconductors. 相似文献
7.
Let S be the semigroup on \(L_2({{\bf R}}^d)\) generated by a degenerate elliptic operator, formally equal to \(- \sum \partial_k \, c_{kl} \, \partial_l\), where the coefficients c kl are real bounded measurable and the matrix C(x)?=?(c kl (x)) is symmetric and positive semi-definite for all x?∈?R d . Let Ω???R d be a bounded Lipschitz domain and μ?>?0. Suppose that C(x)?≥?μ I for all x?∈?Ω. We show that the operator P Ω S t P Ω has a kernel satisfying Gaussian bounds and Gaussian Hölder bounds, where P Ω is the projection of \(L_2({{\bf R}}^d)\) onto L 2(Ω). Similar results are for the operators u ? χ S t (χ u), where \(\chi \in C_{\rm b}^\infty({{\bf R}}^d)\) and C(x)?≥?μI for all \(x \in {\mathop{\rm supp}} \chi\). 相似文献
8.
El Maati Ouhabaz 《Journal of Functional Analysis》2006,238(1):278-297
We consider general Schrödinger operators on domains of Riemannian manifolds with possibly exponential volume growth. We prove sharp large time Gaussian upper bounds. These bounds are then used to prove new Lp-Lp estimates for the corresponding semigroups. Applications to semi-linear parabolic equations are given. 相似文献
9.
Let M be a general complete Riemannian manifold and consider a Schr?dinger operator −Δ+V on L
2(M). We prove Cwikel–Lieb–Rozenblum as well as Lieb–Thirring type estimates for −Δ+V. These estimates are given in terms of the potential and the heat kernel of the Laplacian on the manifold. Some of our results
hold also for Schr?dinger operators with complex-valued potentials. 相似文献
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