On the Existence of Extremals for the Sobolev Trace Embedding Theorem with Critical Exponent

In this paper, the existence problem is studied for extremalsof the Sobolev trace inequality W^1,p()L^p*(), where is a boundedsmooth domain in R^N, p*=p(N–1)/(N–p), is the criticalSobolev exponent, and 1 < p < N. 2000 Mathematics SubjectClassification 35J65 (primary), 35B33 (secondary).     

On Some Properties of Extremals in a Variational Problem Generated by the Sobolev Embedding Theorem

Some properties of extremal functions in the inequality are studied. Bibliography: 10 titles.     

On an Embedding Theorem

We prove a theorem giving conditions under which a discrete-time dynamical system as (x _t ,y _t ) = (f;(x _{t – 1}, y _{t – 1}), g(x _{t – 1}, y _{t – 1})) can be reconstructed from a scalar valued time series ( _t ) _t , which depends only on x _t where _t = (x _t ). This theorem allows us to use the delay-coordinate method in this setting.     

关于实对称矩阵的基本定理

重新证明了实对称矩阵的基本定理:对于任意一个实对称矩阵A,存在实正交矩阵T,使得T′AT成对角形.     

Symmetry Breaking of Extremals for the Caffarelli-Kohn-Nirenberg Inequalities in a Non-Hilbertian Setting

We provide an explicit necessary condition to have that no extremal for the best constant in the Caffarelli-Kohn-Nirenberg inequality is radially symmetric.     

General Embedding Theorem

The quotient space of an arbitrary Banach space B by any subspace B₁ ? B equipped with the norm \(||b|B/{B_1}|| = \mathop {\inf }\limits_{f \in B/{B_1}} ||f|b||\) is considered. In the case where the infimum is a minimum, i.e., it is attained at some element, a formula for this element is presented. The proof is based on restating the original problem in dual spaces with the help of corresponding Legendre transforms. Although the original problem is nonlinear, it is found that its formulation in dual spaces is always linear and solvable. The results are applied to the general theory of boundary value problems for differential equations of mathematical physics.     

前缀码的嵌入定理

设X*是字母表X上的自由幺半群,以X*为顶点集构造一个语言图Γ(X*),引入语言图Γ(X*)的横截集的概念,给出了前缀码嵌入到极大前缀码的一个构造.     

On the Constancy of the Extremal Function in the Embedding Theorem of Fractional Order

Functional Analysis and Its Applications - We consider the problem of the constancy of the minimizer in the fractional embedding theorem $$mathcal{H}^s(Omega) hookrightarrow L_q(Omega)$$ for a...     

On Zippin's Embedding Theorem of Banach spaces into Banach spaces with bases

We present a new proof of Zippin's Embedding Theorem, that every separable reflexive Banach space embeds into one with shrinking and boundedly complete basis, and every Banach space with a separable dual embeds into one with a shrinking basis. This new proof leads to improved versions of other embedding results.     

The Embedding Theorem for Cantor Varieties

Let m and n be fixed integers, with 1 m < n. A Cantor variety C _m,n is a variety of algebras with m n-ary and n m-ary basic operations which is defined in a signature ={g₁,...,g_m,f₁,...,f_n} by the identities f_ig₁x₁,...,x_n),...,g_mx₁,...,x_n) = x_i, _i=1,...,n, g_jf₁x₁,...,x_m),...,f_nx₁,...,x_m)) = x_j, _j=1,...,m. We prove the following: (a) every partial C _m,n-algebra A is isomorphically embeddable in the algebra G= A; S(A) of C _m,n; (b) for every finitely presented algebra G= A; S in C _m,n, the word problem is decidable; (c) for finitely presented algebras in _{C m}, the occurrence problem is decidable; (d) _{C m,n} has a hereditarily undecidable elementary theory.     

Embedding Theorem on Spaces of Homogeneous Type

In [5] the embedding theorem for the Besov spaces Bdot^\A,q_pBdot^{\A,q}_p with $\minus \varepsilon < \alpha \varepsilon $\minus \varepsilon < \alpha \varepsilon and 1 ￡ p1 \le p, q ￡ ￥q \le \infty, and Triebel-Lizorkin spaces \Fdot^\A,q_p\Fdot^{\A,q}_p with $\minus \varepsilon < \alpha \varepsilon $\minus \varepsilon < \alpha \varepsilon and 1 ￡ p1 \le p, q ￡ ￥q \le \infty, on spaces of homogeneous type was obtained. In this article the embedding theorem is generalized to the Besov spaces Bdot^\A,q_pBdot^{\A,q}_p with $p_0 < p \le \infty $p_0 < p \le \infty and 0 < q \le \infty for for p_0 < 1, and the Triebel-Lizorkin spaces, and the Triebel-Lizorkin spaces \Fdot^{\A,q}_pwith with p_1 < p < \inftyand and p_1 < q < \infty for for p_1< 1. The proofs are new even for. The proofs are new even for \mathbb{R}^n$.     

An Embedding Theorem for Abelian Monoidal Categories

We show that, with some technical conditions, an Abelian monoidal category admits a monoidal embedding into the category of bimodules over a ring. The case of semisimple rigid monoidal categories is studied in more detail.     

An Embedding Theorem for Pseudoconvex Domains in Banach Spaces

We show that a pseudoconvex open subset of a Banach space with an unconditional basis is biholomorphic to a closed direct submanifold of a Banach space with an unconditional basis.This research supported in part by NSF grant DMS-0203072 and a Bilsland Dissertation Fellowship from the Graduate School of Purdue University. This paper is the result of my thesis research under the direction of László Lempert, and I would like to thank him for his patient and wise guidance. I would also like to thank Andreas Defant and David Pérez-García for their suggestions regarding tensor products and directing me to the paper [4], and Steve Bell for his suggestions.     

Lipschitz曲线上Besov-Triebel-Lizorkin空间的嵌入定理

本文用离散的Calderón型再生公式。证明了Lipschitz曲线上Beasov空间与Triebel-Lizorkin空间的嵌入定理。     

An Embedding Theorem for Automorphism Groups of Cartan Geometries

We study the automorphism group of a Cartan geometry, and prove an embedding theorem analogous to a result of Zimmer for automorphism groups of G-structures. Our embedding theorem leads to general upper bounds on the real rank or nilpotence degree of a Lie subgroup of the automorphism group. We prove that if the maximal real rank is attained in the automorphism group of a geometry of parabolic type, then the geometry is flat and complete.     

The Bers-Greenberg Theorem and the Maskit Embedding for Teichmuller Spaces

The Bers–Greenberg theorem tells us that the Teichmüllerspace of a Riemann surface with branch points (orbifold) dependsonly on the genus and the number of special points, and noton the particular ramification values. On the other hand, theMaskit embedding provides a mapping from the Teichmüllerspace of an orbifold, into the product of one-dimensional Teichmüllerspaces. In this paper we prove that there is a set of isomorphismsbetween one-dimensional Teichmüller spaces that, when restrictedto the image of the Teichmüller space of an orbifold underthe Maskit embedding, provides the Bers–Greenberg isomorphism.