查看更多>>摘要：In various Hilbert spaces of analytic functions on the unit disk,we charac-terize when a function has optimal polynomial approximants given by truncations of a single power series or,equivalently,when the approximants stabilize.We also intro-duce a generalized notion of optimal approximant and use this to explicitly compute orthogonal projections of 1 onto certain shift invariant subspaces.
查看更多>>摘要：In this paper,we establish global C2 estimates to the Neumann problem for a class of fully nonlinear elliptic equations.As an application,we prove the existence and uniqueness of k-admissible solutions to the Neumann problems.
查看更多>>摘要：We study the existence of standing waves of fractional Schrödinger equa-tions with a potential term and a general nonlinear term:iut-(-△)su-V(x)u+f(u)=0,(t,x)∈ R+× RN,where s ∈(0,1),N＞2s is an integer and V(x)≤ 0 is radial.More precisely,we investigate the minimizing problem with L2-constraint:E(α)=inf{1/2∫RN|(-△)s2u|2+V(x)|u|2-2F(|u|)u ∈ Hs(RN),||u||2L2(RN)=α}.Under general assumptions on the nonlinearity term f(u)and the potential term V(x),we prove that there exists a constant α0 ≥ 0 such that E(α)can be achieved for allα＞αo,and there is no global minimizer with respect to E(α)for all 0＜α＜α0.Moreover,we propose some criteria determining α0=0 or α0＞0.
查看更多>>摘要：In the present note,we consider the problem:how many interpolation nodes can be deleted from the Newman-type rational function such that the convergence rate still achieve.
查看更多>>摘要：In this paper,using the atomic decomposition of the Herz-Morrey-Hardy spaces with variable exponent,the wavelet characterization by means of a local version of the discrete tent spaces with variable exponent is established.As an application,the boundedness of the fractional integral operators from variable exponent Herz-Morrey-Hardy spaces into variable exponent Herz-Morrey spaces is obtained.
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