Absolute Continuity of the Spectrum of a Periodic Schrödinger Operator

We prove the absolute continuity of the spectrum of the Schrödinger operator in , , with periodic (with a common period lattice ) scalar and vector potentials for which either , , or the Fourier series of the vector potential converges absolutely, , where is an elementary cell of the lattice , for , and for , and the value of is sufficiently small, where and otherwise, , and .     

Asymptotic behavior of solutions of A 2nth order nonlinear differential equation

In this paper we prove two results. The first is an extension of the result of G. D. Jones [4[:Every nontrivial solution for

Trajectory and Global Attractors of Three-Dimensional Navier--Stokes Systems

We construct the trajectory attractor of a three-dimensional Navier--Stokes system with exciting force . The set consists of a class of solutions to this system which are bounded in , defined on the positive semi-infinite interval of the time axis, and can be extended to the entire time axis so that they still remain bounded-in- solutions of the Navier--Stokes system. In this case any family of bounded-in- solutions of this system comes arbitrary close to the trajectory attractor . We prove that the solutions are continuous in t if they are treated in the space of functions ranging in . The restriction of the trajectory attractor to , , is called the global attractor of the Navier--Stokes system. We prove that the global attractor thus defined possesses properties typical of well-known global attractors of evolution equations. We also prove that as the trajectory attractors and the global attractors of the -order Galerkin approximations of the Navier--Stokes system converge to the trajectory and global attractors and , respectively. Similar problems are studied for the cases of an exciting force of the form depending on time and of an external force rapidly oscillating with respect to the spatial variables or with respect to time .     

Sharp Conditions for the CLT of Linear Processes in a Hilbert Space

In this paper we study the behavior of sums of a linear process associated to a strictly stationary sequence with values in a real separable Hilbert space and are linear operators from H to H. One of the results is that satisfies the CLT provided are i.i.d. centered having finite second moments and . We shall provide an example which shows that the condition on the operators is essentially sharp. Extensions of this result are given for sequences of weak dependent random variables under minimal conditions.     

Finite splitting fields of normal subgroups

Let G be a finite group, a normal subgroup, p a prime, a finite splitting field of characteristic p for G and We prove that is a splitting field for N, using the action of the Galois group of the field extension on the irreducible representations of N. As is a splitting field for the symmetric group S_n we get as a corollary that is a splitting field for the alternating group A_n. Received: 31 July 2003     

On the Point Spectrum of Self-Adjoint Operators That Appears under Singular Perturbations of Finite Rank

We discuss purely singular finite-rank perturbations of a self-adjoint operator A in a Hilbert space . The perturbed operators are defined by the Krein resolvent formula , Im z 0, where B _z are finite-rank operators such that dom B _z dom A = |0}. For an arbitrary system of orthonormal vectors satisfying the condition span | _i } dom A = |0} and an arbitrary collection of real numbers , we construct an operator that solves the eigenvalue problem . We prove the uniqueness of under the condition that rank B _z = n.     

Quotient Groups of Groups of Certain Classes

For an arbitrary variety of groups and an arbitrary class of groups that is closed on quotient groups, we prove that a quotient group G/N of the group G possesses an invariant system with - and -factors (respectively, is a residually -group) if G possesses an invariant system with - and -factors (respectively, is a residually -group) and N (respectively, N is a maximal invariant -subgroup of the group G).     

Bernstein-Type Theorems and Uniqueness Theorems

Let be an entire function of finite type with respect to finite order and let be a subset of an open cone in a certain n-dimensional subspace (the smaller , the sparser ). We assume that this cone contains a ray 0} \right\}$$ " align="middle" border="0"> . It is shown that the radial indicator of at any point may be evaluated in terms of function values at points of the discrete subset . Moreover, if tends to zero fast enough as over , then this function vanishes identically. To prove these results, a special approximation technique is developed. In the last part of the paper, it is proved that, under certain conditions on and , which are close to exact conditions, the function bounded on is bounded on the ray.     

On Large Deviations of Vector-Valued Additive Functions of a Markov Gaussian Field

We prove a local limit theorem for large deviations of the sums , where , is a Markov Gaussian random field, is a bounded vector-valued function, and . This paper generalizes the paper [13].     

Conservativeness and Extensions of Feller Semigroups

Let denote a Feller semigroup on , and itsextension to the bounded measurable functions. We show that . If the generator of the semigroup is a pseudo-differential operator we can restate this condition in terms of the symbol. As a by-product, we obtain necessary and sufficient conditions for the conservativeness of the semigroup which are again expressed through the symbol.     

Brownian Martingales and Some New Results on Interpolation of Hardy Spaces

Let H₁( ) be the usual Hardy space on . We show that the couple (H₁( ), L( ) is a Calderón couple. This result immediately follows from the following stronger one: Given any fH₁( ) +L( ) there exist two linear operators U and V satisfying the properties: (i) Uf=Nf (Nf being the non-tangential maximal function of f) and U is contractive from H₁( ) to L₁( ) and also from L( ) to L( ); (ii) V(Nf)=f, V is similtaneously bounded from L₁( ) to H₁( ) and from L( ) to L( ) and the norms of V on these spaces are controlled by a universal constant. We also have similar results on the couple (L_p( ), BMO ( )) for every 1相似文献   

K-Theory for the Banach Algebra of Operators on James''s Quasi-reflexive Banach Spaces

We prove that the K-groups of the Banach algebra of bounded, linear operators on the pth James space , where 1 < p < , are given by and . Moreover, for each Banach space and each non-zero, closed ideal contained in the ideal of inessential operators, we show that and . This enables us to calculate the K-groups of for each Banach space which is a direct sum of finitely many James spaces and -spaces.     

The type set for some measures on \mathbb{R}^{2n} with n-dimensional support

Let be realhomogeneous functions in ofdegree and let bethe Borel measure on given by

Smooth Solution of the Dirichlet Problem for a Quasilinear Hyperbolic Equation of the Second Order

On the basis of the exact solution of the linear Dirichlet problem , we obtain conditions for the solvability of the corresponding Dirichlet problem for the quasilinear equation u _tt – u _xx = f(x, t, u, u _t).     

Lattices of interpretability types of varieties

Let be the set of all primes, the field of all algebraic numbers, and Z the set of square-free natural numbers. We consider partially ordered sets of interpretability types such as , and , where AD is a variety of -divisible Abelian groups with unique taking of the pth root _p(x) for every p , is a variety of -modules over a normal field , contained in , and G_n is a variety of n-groupoids defined by a cyclic permutation (12 ...n). We prove that , and are distributive lattices, with and where ub and ub_f are lattices (w.r.t. inclusion) of all subsets of the set and of finite subsets of , respectively.Deceased.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 198–210, March–April, 2005.     

Multidimensional Lagrange–Yen-Type Interpolation Via Kotel'nikov–Shannon Sampling Formulas

Direct finite interpolation formulas are developed for the Paley–Wiener function spaces and , where contains all bivariate entire functions whose Fourier spectrum is supported by the set = Cl{(u, v) |u| + |v| < ], while in the Fourier spectrum support set of its d-variate entire elements is [–, ] ^d . The multidimensional Kotel'nikov–Shannon sampling formula remains valid when only finitely many sampling knots are deviated from the uniform spacing. By using this interpolation procedure, we truncate a sampling sum to its irregularly sampled part. Upper bounds of the truncation error are obtained in both cases.According to the Sun–Zhou extension of the Kadets -theorem, the magnitudes of deviations are limited coordinatewise to . To avoid this inconvenience, we introduce weighted Kotel'nikov–Shannon sampling sums. For , Lagrange-type direct finite interpolation formulas are given. Finally, convergence-rate questions are discussed.     

On the LIL for Self-Normalized Sums of IID Random Variables

Let be i.i.d. random variables and let, for each and . It is shown that a.s. whenever the sequence of self-normalized sums S _n /V _n is stochastically bounded, and that this limsup is a.s. positive if, in addition, X is in the Feller class. It is also shown that, for X in the Feller class, the sequence of self-normalized sums is stochastically bounded if and only if      

A Delocalization Property for Assembly Maps and an Application in Algebraic K-Theory of Group Rings

Let be a group, F the free -module on the set of finite order elements in , with acting by conjugation, and the ring extension of by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaWaaiWaaeaada% WcaaqaaiaaigdaaeaatCvAUfKttLearyGqLXgBG0evaGqbciab-5ga% UbaaieaacaGFLbGaaGOmaiaabc8acqWFPbqAcaqGVaGae8NBa42aaq% qaaeaacqGHdicjcqaHZoWzcqGHiiIZcqqHtoWrcaqGGaGaae4Baiaa% bAgacaqGGaGaae4BaiaabkhacaqGKbGaaeyzaiaabkhacaqGGaGae8% NBa4gacaGLhWoaaiaawUhacaGL9baaaaa!563E!\[\left\{ {\frac{1}{n}e2{\text{\pi }}i{\text{/}}n\left| {\exists \gamma \in \Gamma {\text{ of order }}n} \right.} \right\}\]. For a ring R with , we build an injective assembly map , detected by the Dennis trace map. This is proved by establishing a delocalization property for the assembly map in Hochschild homology, namely providing a gluing of simpler assembly maps (i.e. localized at the identity of ) to build , and by delocalizing a known assembly map in K-theory to define . We also prove the delocalization property in cyclic homology and in related theories.     

Scalar Operators Representable as a Sum of Projectors

We study sets there exist n projectors P₁,...,P_n such that . We prove that if n 6, then .