Weakly Outer Inner Functions

An inner function I in the unit ball B_nB_nⁿ is said to be weakly outer if the closed subspace I H ^p(B ⁿ) is weakly dense in the Hardy space H^p(B ⁿ), 0n for all n1. We also investigate inner functions I such that the subspace IH^p(B ⁿ) is not weakly dense in H^p(B ⁿ).     

Bounded Cyclic Functions in the Ball

With the help of the H²-corona theorem we obtain a sufficient condition for cyclicity in the Bergman space A¹ in the ball. Bibliography: 5 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 303, 2003, pp. 102–110.     

Multipliers for logarithmic Cauchy integrals in the ball

Let B _n denote the unit ball in \mathbbC \mathbb{C} ⁿ , n ≥ 1. Let K \mathcal{K} ₀(n) denote the class of functions defined for z ∈ B _n as a constant plus the integral of the kernel log(1/(1 −〈z, ζ〉)) against a complex Borel measure on the sphere {ζ ∈ \mathbbC \mathbb{C} ⁿ ,: |ζ| = 1}. Properties of holomorphic functions g such that fg ∈ K \mathcal{K} ₀(n) for all f ∈ K \mathcal{K} ₀(n) are studied. The extended Cesàro operators are investigated on the spaces K \mathcal{K} ₀(n), n ≥ 1. Bibliography: 15 titles.     

关于Hirota-Satsuma系统初值问题的局部和整体适定性

本文利用ＫＤＶ方程所对应的线性方程解所具有的光滑效应及压缩映像原理,得到了Ｈｉｒｏｔａ－Ｓａｔｓｕｍａ系统初值问题的局部和整体适定性结果．     

Radial limits of positive solutions to the Darboux equation

Assume that a positive function u satisfies the Darboux equation

Overlapping B3Π0u ← X1Σ g/+ and 1Π1u ← X1Σ g/+ non-radiative characteristic of Br2 vapour in the wavelength region 505–541 nm

The vibronic vapour phase photoacoustic spectrum of Br₂ in the wavelength region 505–541 nm (19796–18480 cm⁻¹) has been recorded using microphone as well as pump-probe method. Discrete vibronic bands superimposed on a monotonically increasing continuum background towards the dissociation limit results from the overlapping B ³Π _0u ^/+ ← X ¹Σ _g ^/+ and ¹Π_1u ← X ¹Σ _g ^/+ electronic transitions. Vibronic bands originating from υ″=0 have been used to estimate the relative rate of non-radiative relaxation as a function of the excited state B ³Π_0u vibrational quantum number υ′. A comparison with the optical absorption spectroscopy of Br₂ leads to the identification of three broad spectral regions between 505 and 541 nm (19796 and 18480 cm⁻¹) on the basis of different non-radiative relaxation processes.     

Bloch, Hardy, and BMOA spaces in the ball

We construct a little Bloch function that belongs to all Hardy spaces H^p, p < ∞, but not to BMOA in the unit ball of ℂⁿ. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2005, pp. 74–77.     

Weighted composition operators into Lipschitz spaces

We study bounded and compact weighted composition operators that map into holomorphic Lipschitz spaces. Bibliography: 11 titles.     

Slow relaxation processes in nematic liquid crystals at weak surface anchoring

We present new results of experimental investigations of azimuthal director reorientation dynamics for a nematic liquid crystal on solid substrates. Two types of substrate with weak anchoring were studied: glass/polystyrene and glass/UV-activated dye. Slow and fast relaxation processes were observed in both cases under the action of a strong 'in-plane' electric field. The slow surface reorientation and memory effects were controlled by two parameters: the electric voltage and the excitation time. It was established that the increase of the excitation time results in a slowing of the relaxation of the system to the initial state after turning off the electric field. A phenomenological model of a gliding of easy axes is proposed to explain the slow relaxation process.     

Regular Unitarily Invariant Spaces on the Complex Sphere

Let K be a compact space, let X be a closed subspace of C(K), and let be a positive measure on K. The triple is said to be regular if, for any positive function and for any , there exists a function such that on K and . The case where K is the unit sphere in and the subspace X is invariant with respect to the unitary group is investigated. Sufficient spectral conditions and a necessary condition for the regularity of a triple are obtained. Connections with compactness of certain Hankel operators and applications to interpolation problems are presented. Bibliography: 16 titles.