Given an SO(3)-bundle with connection, the associated two-sphere bundle carries a natural closed 2-form. Asking that this be symplectic gives a curvature inequality first considered by Reznikov [34]. We study this inequality in the case when the base has dimension four, with three main aims. Firstly, we use this approach to construct symplectic six-manifolds with c1 = 0 which are never Kähler; ...

X iv :0 90 5. 40 67 v1 [ m at h. FA ] 2 5 M ay 2 00 9 BESSEL TYPE INEQUALITIES IN HILBERT C-MODULES S. S. DRAGOMIR, M. KHOSRAVI AND M. S. MOSLEHIAN Abstract. Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombiari and Boas–Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C∗-mo...

Given a real valued random variable Θ we consider Borel measures μ on B(R), which satisfy the inequality μ(B) ≥ Eμ(B−Θ) (B ∈ B(R)) (or the integral inequality μ(B) ≥ R∞ −∞ μ(B−h)γ(dh)). We apply the Choquet theorem to obtain an integral representation of measures μ satisfying this inequality. We give integral representations of these measures in the particular cases of the random variable Θ.

In this paper we study upper bounds for the density of solution to stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/3. We show that under some geometric conditions, in the regular case H > 1/2, the density of the solution satisfies the log-Sobolev inequality, the Gaussian concentration inequality and admits an upper Gaussian bound. In the rough...

The classical embedding theorem of Carleson deals with finite positive Borel measures μ on the closed unit disk for which there exists a positive constant c such that ‖f‖L2(μ) ≤ c‖f‖H2 for all f ∈ H, the Hardy space of the unit disk. Lefèvre et al. examined measures μ for which there exists a positive constant c such that ‖f‖L2(μ) ≥ c‖f‖H2 for all f ∈ H. The first type of inequality above was e...

Abstract In this paper we investigate Ramanujan’s inequality concerning the prime counting function, asserting that ? ( x 2 ) < e log \pi \left( {{x^2...

We prove the inequality h(x)~ G(x, y)h(y) < cG(x, y) +c, where G is the Green function of a plane domain D , h is positive and harmonic on D , and c is a constant whose value depends on the topological nature of the domain. In particular, for the class of proper simply connected domains c may be taken to be an absolute constant. As an application, we prove the Conditional Gauge Theorem for plan...

If T is a complex symmetric operator on a separable complex Hilbert space H, then the spectrum σ(|T |) of √ T ∗T can be characterized in terms of a certain approximate antilinear eigenvalue problem. This approach leads to a general inequality (applicable to any bounded operator T : H → H), in terms of the spectra of the selfadjoint operators ReT and ImT , restricting the possible location of el...

The H∞ dynamic output feedback controller design of linear neutral delay systems is studied using Lyapunov-Krasovskii stability theory and linear matrix inequality approach. Based on feasibility positive definite solution to the linear matrix inequalities, we first develop a delay-independent stability criterion and a sufficient condition which makes the system asymptotically stable and guarant...

We establish conditions under which the extended Hardy-Littlewood inequality ∫ RN H ( |x|, u1(x), . . . , um(x) ) dx ≤ ∫ RN H ( |x|, u1(x), . . . , um(x) ) dx, where each ui is non-negative and u ∗ i denotes its Schwarz symmetrization, holds. We also determine appropriate monotonicity assumptions on H such that equality occurs in the above inequality if and only if each ui is Schwarz symmetric....