Stability of solutions to the Cauchy problem for a plane hyperbolic system with time-periodic coefficients

Considering a plane hyperbolic system with time-periodic coefficients, we construct a version of the direct Lyapunov method with the condition on the derivative of the Lyapunov functional along the trajectories of the system which is weakened by use of periodicity of the coefficients. We exhibit an illustrative example.     

Quasi-compactness and absolutely continuous kernels

We show how the essential spectral radius r _e (Q) of a bounded positive kernel Q, acting on bounded functions, is linked to the lower approximation of Q by certain absolutely continuous kernels. The standart Doeblin’s condition can be interpreted in this context, and, when suitably reformulated, it leads to a formula for r _e (Q). This results may be used to characterize the Markov kernels having a quasi-compact action on a space of measurable functions bounded with respect to some test function, when no irreducibilty and aperiodicity are assumed.      

Well-posedness of general nonlocal nonhomogeneous boundary value problems for pseudodifferential equations with partial derivatives

In the article we study the questions of well-posedness of general nonlocal boundary value problems for pseudodifferential equations in the Besov-type limit spaces.     

Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation

We consider the problem of describing the possible spectra of an acoustic operator with a periodic finite-gap density. On the moduli space of algebraic Riemann surfaces, we construct flows that preserve the periods of the corresponding operator. By a suitable extension of the phase space, these equations can be written with quadratic irrationalities. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 1, pp. 46–57, October, 2007.     

The characteristic of noncompact convexity and random fixed point theorem for set-valued operators

Let (Ω, Σ) be a measurable space, X a Banach space whose characteristic of noncompact convexity is less than 1, C a bounded closed convex subset of X, KC(C) the family of all compact convex subsets of C. We prove that a set-valued nonexpansive mapping T: C → KC(C) has a fixed point. Furthermore, if X is separable then we also prove that a set-valued nonexpansive operator T: Ω × C → KC(C) has a random fixed point.     

A Galois Connection

The connection presented in this paper mirror-links two metamathematical structures, the finitary closure operators, and the compact consistency properties, in such a way that a specification of one structure induces a provably equivalent specification of the other. Mathematics Subject Classification (2000): Primary 06A15, Secondary 28E10 03B22     

Interpolation of positive operators

We study problems of interpolation of positive linear operators in couples of ordered Banach spaces. From this viewpoint, we study couples of noncommutative spaces L ₁, L _∞ associated with weights and traces on von Neumann algebras.     

次可分解算子的不变子空间格的丰富性

证明了一类次可分解算子的不变子空间格是丰富的,并举例说明存在Hilbert空间上的有界线性算子T,它有无穷多个不变子空间,但是它的不变子空间格Lat(T)不丰富．     

序Banach空间中一类算子方程的可解性

利用改进的Mnch紧性条件,研究了一类算子方程Lx=Nx的解的存在性．本文结果并没有要求算子L和N的连续性．作为应用,讨论了右端项不连续的隐式椭圆偏微分方程的边值问题的解的存在性．