THE EXTENSION THEOREMS OF CONE LINEAR OPERATORS

A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators is given.

Polynomials,Higher Order Sobolev Extension Theorems and Interpolation Inequalities on Weighted Folland-Stein Spaces on Stratified Groups

This paper consists of three main parts.One of them is to develop local and global Sobolev interpolation inequalities of any higher order for the nonisotropic Sobolev spaces on stratified nilpotent Lie groups.Despite the extensive research after Jerison’s work[3]on Poincaré-type inequalities for Hrmander’s vector fields over the years,our results given here even in the nonweighted case appear to be new.Such interpolation inequalities have crucial applications to subelliptic or parabolic PDE’s involving vector fields.The main tools to prove such inequalities are approximating the Sobolev func- tions by polynomials associated with the left invariant vector fields on G.Some very useful properties for polynomials associated with the functions are given here and they appear to have independent interests in their own rights.Finding the existence of such polynomials is the second main part of this paper.Main results of these two parts have been announced in the author’s paper in Mathematical Research Letters[38]. The third main part of this paper contains extension theorems on anisotropic Sobolev spaces on stratified groups and their applications to proving Sobolev interpolation inequalities on(εδ)domains. Some results of weighted Sobolev spaces are also given here.We construct a linear extension operator which is bounded on different Sobolev spaces simultaneously.In particular,we are able to construct a bounded linear extension operator such that the derivatives of the extended function can be controlled by the same order of derivatives of the given Sobolev functions.Theorems are stated and proved for weighted anisotropic Sobolev spaces on stratified groups.

AN EXTENSION OF BROSOWSKI-MEINARDUS THEOREM ON INVARIANT APPROXIMATION

We obta(?) gener(?)ization of a fixed point th(?)of Dotson for nan-expansive mapptngs on star-sba p(?)sets and then(?)it to Prooe a unified Brosowski-M(?)us theorem on in(?)ariant approximatton in the setting,(?)fp-normed line(?)spaces.

L^(2) EXTENSIONS WITH SINGULAR METRICS ON K?HLER MANIFOLDS

In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics,and also discuss their applications and the ideas contained in the proofs.

ALGEBRAIC EXTENSION OF *-A OPERATOR

In this paper, we study various properties of algebraic extension of ＊-A operator.Specifically, we show that every algebraic extension of ＊-A operator has SVEP and is isoloid.And if T is an algebraic extension of ＊-A operator, then Weyl＇s theorem holds for f（T）, where f is an analytic functions on some neighborhood of σ（T） and not constant on each of the components of its domain.

Existence of Solutions to Multi-point BVP with p-Laplacian at Resonance

This paper is concerned with the existence of solutions for the following multipoint boundary value problem at resonance{(Φp (x'))' + f(t,x)=0,0 < t < 1,x' (0)=x'(ξ) x(1)=m-3 ∑i=1 βi x(η i),where βi∈ R,m-3 ∑i=1 β i=1,0 < η 1 < η 2 < ··· < ηm-3 < 1,m-3 ∑i=1 βiηi=1,0 < ξ < 1.An existence theorem is obtained by using the extension of Mawhin's continuation theorem.Since almost all the multi-point boundary value problem at resonance in previous papers are for the linear operator without p-Laplacian by the use of Mawhin's continuation theorem,our method is new.

A general extension theorem for cohomology classes on non reduced analytic subspaces

The main purpose of this paper is to generalize the celebrated L^2 extension theorem of Ohsawa and Takegoshi in several directions: The holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety from which the extension is performed may be non reduced, the ambient manifold is K¨ahler and holomorphically convex, but not necessarily compact.

Strong openness of multiplier ideal sheaves and optimal L^2 extension

In this paper, we reveal that our solution of Demailly's strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Koll′ar and Jonsson-Mustat?a implies the truth of twisted versions of the strong openness conjecture; our optimal L^2 extension implies Berndtsson's positivity of vector bundles associated to holomorphic fibrations over a unit disc.

Structure prediction for error pattern and extension of Welch-Berlekamp theorem

As the Welch-Berlekamp (W-B) theorem accurately predicts structure of error locator polynomials of the error patterns, it results in the Welch-Berlekamp algorithm of decoding cyclic codes. However, it is only valid within the BCH bound. Now, a prediction formula for error locator determination is presented based on the study of theory of minimal homogeneous interpolation problem, which extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm so that the constraint from the BCH

A parametric family of quartic Thue equations

In this paper,we give all primitive solutions of a parameterized family of quartic Thue equations:x^(4)-4cx^(3)y+(6c+2)x^(2)y^(2)+4cxy^(3)+y^(4)=96c+169,c>0.

A Characterization of Continuous Module Homomorphisms on Random Semi—Normed Modules and Its Applications

In this paper, a characterization of continuous module homomorphisms on random semi-normed modules is first given; then the characterization is further used to show that the Hahn-Banach type of extension theorem is still true for continuous module homomorphisms on random semi-normed modules.

A comparison of two no-arbitrage conditions

We give a comparison of two no-arbitrage conditions for the fundamental theorem of asset pricing. The first condition is named as the no free lunch with vanishing risk condition and the second the no good deal condition. We aim to derive a relationship between these two conditions.

SOME ESTIMATES WITH NONCONFORMING ELEMENTS IN DOMAIN DECOMPOSITION ANALYSIS

Some essential estimates, especially the so-called extension theorems, are established in this paper, for the nonconforming finite elements with their continuity at the vertices or the edge midpoints of the elements of the quasi-uniform mesh. As in the conforming discrete cases, these estimates play key roles in the theoretical analysis of the nonoverlap domain decomposition methods for the solving of second order self-adjoint elliptic problems discretized by the nonconforming finite element methods.

Characterizations of plurisubharmonic functions

We give characterizations of(quasi-)plurisubharmonic functions in terms of L^(p)-estimates of■and Lp-extensions of holomorphic functions.