Composition Operators on α-Bloch Spaces of the Unit Ball

The authors characterize the boundedness and compactness of composition operators between α-Bloch spaces of the unit ball.     

Composition Operators on H~2

ＣｏｍｐｏｓｉｔｉｏｎＯｐｅｒａｔｏｒｓｏｎＨ￣２ＹｕＤａｈａｉ（余大海）ＣａｏＧｕａｎｇｆｕ（曹广福）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＳｉｃｈｕａｎＵｎｉｖ．，Ｃｈｅｎｇｄｕ，）Ｓｉｃｈｕａｎ，６１００６４ＣｏｍｍｕｎｉｃａｔｅｄｂｙＧｕｏＤａｊｕｎＲ...     

紧Riemann流形的高阶特征值估计

对Ricci曲率具负下界的紧Riemann流形,本文获得了热方程正解优化的梯度估计及Harnack不等式,证明了高阶特征值下界定量估计的猜想．     

Hankel算子与Riemann猜测

本文证明了著名的Ｒｉｅｍａｎｎ猜测等价于单位圆的Ｈａｒｄｙ空间上的某族Ｈａｎｋｅｌ算子的奇异值的单重性．     

A Note on Hermite and Subelliptic Operators

In this note, we compute the fundamental solution for the Hermite operator with singularity at an arbitrary point y∈R^n. We also apply this result to obtain the fundamental solutions for the Grushin operator in R^2 and the sub-Laplacian in the Heisenberg group Hn.     

Riemann曲面上的正常和拟正常复合算子

Riemann曲面M上的平方可测1-形式全体和解析1-形式全体均可构成Hilbert空间.本文讨论Riemann曲面上的解析映射导出的这类Hilbert空间上的复合算子,研究复合算子的正常性、拟正常性的诱导映射特征.特别地,当M有有限三角剖分时,证明了正常复合算子、拟正常复合算子、酉复合算子、等距复合算子和可逆复合算子等价.     

Finite Degree Holomorphic Covers of Compact Riemann Surfaces

A conjecture of Ehrenpreis states that any two compact Riemann surfaces of genus at least two have finite degree unbranched holomorphic covers that are arbitrarily close to each other in moduli space. Here we prove a weaker result where certain branched covers associated with arithmetic Riemann surfaces are allowed, and investigate the connection of our result with the original conjecture.     

Riemann曲面上的正常和拟正常复合算子

Riemann曲面M上的平方可测1-形式全体和解析1-形式全体均可构成Hilbert空间。本文讨论Riemann曲面上的解析映射导出的这类Hilbert空间上的复合算子,研究复合算子的正常性、拟正常性的诱导映射特征。特别地,当M有有限三角剖分时,证明了正常复合算子、拟正常复合算子、酉复合算子、等距复合算子和可逆复合算子等价。     

具有正Ricci曲率紧Riemann流形上的第一特征值估计

M为紧致n维Riemann流形，Ricci曲率具有正下界n-1，d是M的直径，本文证明了其Laplace算子的第一特征值λ1≥π^2/d^2 n-1/2。     

关于完备Riemann流形的本性谱

本文证明一类具非负截曲率完备Riemann流形的Laplace算子的本性谱为(0,+∞)。     

紧Riemann面上的复合算子

In the present paper, the characterization of invertible composition oper-ators on compact Riemann surfaces is obtained, which is very different from that in the case of Hardy or Bergman spaces on a disk of the complex plane C.     

Operators on Differential Form Spaces for Riemann Surfaces

In the present paper, a problem of Ioana Mihaila is negatively answered on the invertibility of composition operators on Riemann surfaces, and it is proved that the composition operator Cp is Predholm if and only if it is invertible if and only if p is invertible for some special cases. In addition, the Toeplitz operators on ∧1 2, a（M） for Riemann surface M are defined and some properties of these operators are discussed.     

解析函数的Banach空间上之复合算子

本文研究了一类解析函数的Ｂａｎａｃｈ空间Ｘ上之复合算子，这类空间包含了Ｂｌｏｃｈ空间，并且可看作Ｂｅｒｇｍａｎ空间Ｌ１ａ（Ｄ）中具有原子分解的解析函数的对偶空间．我们刻划了这类空间上紧复合算子及Ｆｒｅｄｈｏｌｍ复合算子的特征，此外，还研究了具有闭值域的复合算子．     

Fredholm Operators and Riesz Theory for Polynomially Compact Operators

In this article, we give a characterization of a class of bounded Fredholm operators on a Banach space which is developed to present some general existence results of the operators equation of the second kind. The obtained results are used to describe the Riesz–Schauder theory of compact operators in the more general setting of polynomially compact operators.     

Fredholm composition operators on algebras of analytic functions on Banach spaces

We prove that Fredholm composition operators acting on the uniform algebra H^∞(BE) of bounded analytic functions on the open unit ball of a complex Banach space E with the approximation property are invertible and arise from analytic automorphisms of the ball.     

Gromov Hyperbolicity of Riemann Surfaces

We study the hyperbolicity in the Gromov sense of Riemann surfaces. We deduce the hyperbolicity of a surface from the hyperbolicity of its ＂building block components＂. We also prove the equivalence between the hyperbolicity of a Riemann surface and the hyperbolicity of some graph associated with it. These results clarify how the decomposition of a Riemann surface into Y-pieces and funnels affects the hyperbolicity of the surface. The results simplify the topology of the surface and allow us to obtain global results from local information.     

Bergman空间上Toeplitz算子的局部及Fredholm性质

本文讨论了Ｂｅｒｇｍａｎ空间上Ｔｏｅｐｌｉｔｚ算子的局部谱的关系．利用局部化原理给出了Ｔｏｅｐｌｉｔｚ算子拟换位子紧性的一个充分条件．给出了一类符号的Ｔｏｅｐｌｉｔｚ算子是Ｆｒｅｄｈｏｌｍ算子的充分条件．     

Fredholm and Propernes Properties of Quasilinear Elliptic Operators on RN

We discuss the Fredholm and properness properties of second-order quasilinear elliptic operators viewed as mappings from W^2,p( R ^N) to L^p( R ^N) with N < p < ∞. The unboundedness of the domain makes the standard Sobolev embedding theorems inadequate to investigate such issues. Instead, we develop several new tools and methods to obtain fairly simple necessary and suffcient conditions for such operators to be Fredholm with a given index and to be proper on the closed bounded subsets of W^2,p( R ^N). It is noteworthy that the translation invariance of the domain, well-known to be responsible for the lack of compactness in the Sobolev embedding theorems, is taken advantage of to establish results in the opposite direction and is indeed crucial to the proof of the properness criteria. The limitation to second-order and scalar equations chosen in our exposition is relatively unimportant, as none of the arguments involved here relies upon either of these assumptions. Generalizations to higher order equations or to systems are thus clearly possible with a variableamount of extra work. Various applications, notably but not limited, to global bifurcation problems, are described elsewhere.     

Composition operators on a Banach space of analytic functions

In this paper, we study composition operators on a Banach space of analytic functions, denoted byX, which includes the Bloch space. This space arises naturally as the dual space of analytic functions in the Bergman spaceL _α ¹ (D) which admit an atomic decomposition. We characterize the functions which induce compact composition operators and those which induce Fredholm operatorson this space. We also investigate when a composition operator has a closed range. Supported by NNSFC No.19671036