the grace mission has provided scientific community time-variable gravity field solutions with high precision and on a global scale. the grace mission was launched on march 2003. this mission consists of two satellites that pursue each other in their orbit. distance between two satellites in orbit is measured continuously to an accuracy of better than 1 micron using kbr system placed in satelli...

Precise conditions are given under which the real interpolation space [Y0, X1]θ,p coincides with a closed subspace of [X0,X1]θ,p when Y0 is a closed subspace of codimension one. This result is applied to the study of nonharmonic Fourier series in the Sobolev spaces Hs(−π, π) with 0 < s < 1. The main result looks like this: if {eiλnt} is an unconditional basis in L2(−π, π), then there exist two ...

We prove the uniform convergence of the multigrid V -cycle on graded meshes for corner-like singularities of elliptic equations on a bounded domain Ω ⊂ IR. In particular, using some weighted Sobolev space K a (Ω) and the method of subspace corrections with the elliptic projection decomposition estimate on K a (Ω), we show that the multigrid V -cycle converges uniformly for piecewise linear func...

On the n-dimensional hypercube, for given k ∈ N, wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0, 1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and suitable dual wavelets can be constructed to be locally supported. The construction of the isotropic wavelet ...

On the n-dimensional hypercube, for given k ∈ N, biorthogonal wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0, 1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and dual wavelets can be constructed to be locally supported. The construction of the isotropic wave...

We study the nonuniformly elliptic, nonlinear system − div(h1(x)∇u) + a(x)u = f(x, u, v) in R , − div(h2(x)∇v) + b(x)v = g(x, u, v) in R . Under growth and regularity conditions on the nonlinearities f and g, we obtain weak solutions in a subspace of the Sobolev space H1(RN , R2) by applying a variant of the Mountain Pass Theorem.

We give precise conditions under which the real interpolation space [Y0, X1]θ,p coincides with a closed subspace of [X0, X1]θ,p when Y0 is a closed subspace of codimension one. We then apply this result to nonharmonic Fourier series in Sobolev spaces Hs(−π, π) when 0 < s < 1. The main result: let E be a family of exponentials exp(iλnt) and E forms an unconditional basis in L2(−π, π). Then there...

In this paper, we introduce subspace-frequently hypercyclic operators. We show that these operators are subspace-hypercyclic and there are subspace-hypercyclic  operators that are not subspace-frequently hypercyclic. There is a criterion like to subspace-hypercyclicity criterion that implies subspace-frequent hypercyclicity and if an operator $T$ satisfies this criterion, then $Toplus T$ is sub...

Let [Formula: see text] be a compact connected orientable Cauchy–Riemann (CR) manifold with the action of Lie group text]. Under natural pseudoconvexity assumptions we show that CR Guillemin–Sternberg map is an isomorphism at level Sobolev spaces functions, modulo finite-dimensional subspace. As application study this for holomorphic line bundles which are positive near inverse image by momentu...

In this paper we prove that the Benjamin–Ono equation admits an analytic Birkhoff normal form in open neighborhood of zero H0s(T,R) for any s>−1/2 where denotes subspace Sobolev space Hs(T,R) elements with mean 0. As application show −1/2<s<0, flow map S0t:H0s(T,R)→H0s(T,R) is nowhere locally uniformly continuous a H0s(T,R).