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| 1 | THE GROWTH THEOREM FOR STARLIKE MAPPINGS ON BOUNDED STARLIKE CIRCULAR DOMAINS显示文摘The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular domains.This type of domain discussed is rather general, since the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it. In the unit disc, it is just the famous growth and covering theorem for univalent functions.This theorem successfully realizes the initial idea of H. Cartan about how to extend geometric function theory from one variable to several complex variables. | LIU TAISHUN (Department of Mathematics, University of Science and Technology of China, Hefei 230026, China)REN GUANGBIN (Department of Mathematics, University of Science and Technology of China, Hefei 230026, China) | 1998 | Chinese Annals of Mathematics,Series B1998，19，4： | 39 |
| 2 | BERGMAN TYPE OPERATOR ON MIXED NORM SPACES WITH APPLICATIONS显示文摘BERGMANTYPEOPERATORONMIXEDNORMSPACESWITHAPPLICATIONSRENGUANGBINSHIJIHUAIAbstractTheauthorsinvestigatetheconditionsforthebou... | REN GUANGBIN * SHI JIHUAI * | 1997 | Chinese Annals of Mathematics,Series B1997，18，3： | 26 |
| 3 | Jackson’s theorem in Q_p spaces显示文摘A Jackson type inequality in Q p spaces is established, i.e., for any f (z) = Σ∞ j=0 ajzj ∈ Qp , 0≤p < ∞, a > 1, and k-1 ∈ N,where ω(1/k, f, Q p ) is the modulus of continuity in Q p spaces and C(a) is an absolute constant depending only on the parameter a. | CHEN YingWei 1 & REN GuangBin 1, 2, 1 Department of Mathematics, University of Science and Technology of China, Hefei 230026, China 2 Department of Mathematics, University of Aveiro, P-3810-193 Aveiro, Portugal | 2010 | Science China Mathematics2010，53，2： | 6 |
| 4 | Theory of several paravector variables:Bochner-Martinelli formula and Hartogs theorem显示文摘The aim of this article is to extend the theory of several complex variables to the non-commutative realm. Some basic results,such as the Bochner-Martinelli formula,the existence theorem of the solutions to the non-homogeneous Cauchy-Riemann equations,and the Hartogs theorem,are generalized from complex analysis in several variables to Clifford analysis in several paravector variables. In particular,the Bochner-Martinelli formula in several paravector variables unifies the corresponding formulas in the theory of one complex variable,several complex variables,and several quaternionic variables with suitable modifications. | REN GuangBin WANG HaiYan | 2014 | Science China Mathematics2014，57，11： | 4 |
| 5 | Almansi decomposition for Dunkl operators显示文摘Let Ω be a G-invariant convex domain in RN including 0, where G is a Coxeter group associated with reduced root system R. We consider functions f defined in Ω which are Dunkl polyharmonic, i.e. (△h)nf= 0 for some integer n. Here△h= ∑Nj=1D2j is the Dunkl Laplacian, and Dj is the Dunkl operator attached to the Coxeter group G,Djf(x)=(δ)/(δ)xjf(x)+∑v∈R+kvf(x)-f(бvx)/vj,where kv is a multiplicity function on R and σv is the reflection with respect to the root v.We prove that any Dunkl polyharmonic function f has a decomposition of the form f(x)=f0(x)+│x│2f1(x)+…+│x│2(n-1)fn-1(x),(A)x∈Ω,where fj are Dunkl harmonic functions, i.e. △hfj = 0. This generalizes the classical Almansi theorem for polyharmonic functions as well as the Fischer decomposition. | REN Guangbin | 2005 | Science China Mathematics2005，48，z1： | 4 |
| 6 | Octonion Analysis of Several Variables显示文摘The octonions are distinguished in the M-theory in which Universe is the usual Minkowski space R4 times a G2 manifold of very small diameter with G2 being the automorphism group of the octonions.The multidimensional octonion analysis is initiated in this article,which extends the theory of several complex variables,such as the Bochner–Martinelli formula,the theory of non-homogeneous Cauchy–Riemann equations,and the Hartogs principle,to the non-commutative and non-associative realm. | Haiyan Wang Guangbin Ren | 2014 | Communications in Mathematics and Statistics2014，2，2： | 2 |
| 7 | Bicomplex Hermitian Clifford analysis显示文摘,复杂赫米琴·克利福德分析最近作为几个复杂变量的理论的精炼出现了同时,量力学的 bicomplex 版本激发的 bicomplex 数字的理论也在完整的开发中。这刺激我们把赫米琴·克利福德分析与 bicomplex 数字的理论相结合以便建立 bicomplex 赫米琴·克利福德分析的理论。与欧几里德几何学的克利福德分析同时, bicomplex 赫米琴·克利福德分析在 bicomplex 赫米琴·迪拉克操作员附近被集中:\( C ^ \infty ( \mathbb { R }^{ 4n }, \mathbb { W }_{ 4n }) \to C ^ \infty ( \mathbb { R }^{ 4n }, \mathbb { W }_{ 4n })\),在哪儿\( \mathbb { W }_{ 4n }\)是三代数学的张肌产品,即,夸张四元数, bicomplex 数字\( \mathbb { B }\),并且克利福德代数学<潜水艇class=“ a-plus-plus ”> 0,4n 。操作员是拉普拉斯算符在的一条方形的根<啜class=“ a-plus-plus ”> 4n ,与 K 由公式介绍了<潜水艇class=“ a-plus-plus ”>是的 j 基础,并且\( \partial _{ Z_j }\)在 bicomplex 克利福德代数学\表示扭曲的赫米琴·迪拉克操作员( \mathbb { B } \otimes \mathbb { R }_{ 0,4n }\)其定义包含 bicomplex Witt 基础的精细的构造。操作符的介绍能也在建筑群或 quaternionic 背景在赫米琴·克利福德分析打翻占优势的意见建筑群或 quaternionic Hermitiean 单基因的函数被方程的一个系统描述而不是由象是迪拉克的空解决方案的古典单基因的函数一样的一个单个方程操作符。与在 quaternionic 设定的赫米琴·克利福德分析相对照,扭曲的真正的克利福德向量的泊松方括号不在 bicomplex 背景一般来说消失。为操作员,我们建立 Cauchy 不可分的公式,它在几个复杂变量的理论概括 Martinelli-Bochner 公式。 | Bin CHEN Guangbin REN Haiyan WANG | 2015 | Frontiers of Mathematics in China2015，10，3： | 2 |
| 8 | Initiating,growing and cracking of hydrogen blisters显示文摘The growing process of a hydrogen blister in a wheel steel was observed in situ with an optical microscope, and the fracture surfaces formed from broken blisters on a wheel steel and bulk metallic glass were investigated. The initiating, growing, cracking and breaking of hydrogen blis-ters are as follows. Supersaturated vacancies can increase greatly during charging and gather together into a vacancy cluster (small cavity). Hydrogen atoms become hydrogen molecules in the vacancy cluster and hydrogen molecules can stabilize the vacancy cluster. The small cavity becomes the nucleus of hydrogen blister. The blister will grow with enter-ing of vacancies and hydrogen atoms. With increasing hy-drogen pressure, plastic deformation occurs first, the hydro-gen blister near the surface extrudes, and then cracks initiate along the wall of the blister with further increasing hydrogen pressure. A cracked blister can grow further through propa-gating of cracks until it breaks. | REN Xuechong SHAN Guangbin CHU Wuyang SU Yanjing GAO Kewei QIAO Lijie JIANG Bo CHEN Gang CUI Yinhui | 2005 | Chinese Science Bulletin2005，50，17： | 2 |
| 9 | Howe duality in Dunkl superspace显示文摘In the framework of superspace in Clifford analysis for the Dunkl version, the Fischer decomposition is established for solutions of the Dunkl super Dirac operators. The result is general without restrictions on multiplicity functions or on super dimensions. The Fischer decomposition provides a module for the Howe dual pair G × osp(1|2) on the space of spinor valued polynomials with G the Coxeter group, while the generators of the Lie superspace reveal the naturality of the Fischer decomposition. | REN GuangBin 1,2 1 Department of Mathematics, University of Science and Technology of China, Hefei 230026, China 2 Department of Mathematics, University of Aveiro, Aveiro 3810-193, Portugal | 2010 | Science China Mathematics2010，53，12： | 1 |
| 10 | Gleason’s problem in weighted Bergman space on egg domains显示文摘 | Guangbin Ren Jihuai Shi | 1998 | Science in China Series A: Mathematics1998，，3： | 1 |
| 11 | Growth theorem of convex mappings on bounded convex circular domains显示文摘 | Taishun Liu Guangbin Ren | 1998 | Science in China Series A: Mathematics1998，，2： | 1 |
| 12 | Coefficient multipliers of mixed norm space in the ball显示文摘In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (Hp,q(ψ1),Hu,v(ψ2)) for the values of p,q,u,v in three cases: (i) 0 < p ≤ u ≤∞, 0 < q ≤min(1,v) ≤∞. (ii) v= ∞,0 < p ≤ u ≤∞, 1 ≤ u,q ≤∞. (iii) 1 ≤ v ≤ 2 ≤ q ≤∞, and 0 < p ≤ u ≤∞ or 1 ≤ p,u ≤∞. The first case extends the result of Blasco, Jevti(c), and Pavlovi(c) in one variable. The third case generalizes partly the results of Jevti(c), Jovanovi(c), and Wojtaszczyk to higher dimensions. | SHI Jihuai REN Guangbin | 2006 | Science China Mathematics2006，49，11： | 1 |
| 13 | Gleason’s problem in weighted Bergman space on egg domains显示文摘 | Guangbin Ren Jihuai Shi | 1998 | Science in China Series A: Mathematics1998，，3： | 1 |
| 14 | Almansi decomposition for Dunkl operators显示文摘 | Guangbin Ren | 2005 | Science in China Series A: Mathematics2005，，1： | 1 |
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