In this paper, we give an explicit formula of the Bergman kernel function on Hua Construction of the second type when the parameters 1/p1,…, 1/pr-1 are positive integers and 1/pr is an arbitrary positive real number.
The authors give the condition that the Bergman kernel function on the first type of Cartan-Hartogs domain exists zeros.If the Bergman kernel function of this type of domain has zeros,the zero set is composed of sever...The authors give the condition that the Bergman kernel function on the first type of Cartan-Hartogs domain exists zeros.If the Bergman kernel function of this type of domain has zeros,the zero set is composed of several path-connected branches,and there exists a continuous curve to connect any two points in the non-zero set.展开更多
The boundary behavior of the Bergman kernel function of a kind of Reinhardt domain is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points ( Z, Z) Let Q be the Reinhardt dom...The boundary behavior of the Bergman kernel function of a kind of Reinhardt domain is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points ( Z, Z) Let Q be the Reinhardt domainwhere is the Standard Euclidean norm in and let K( Z, W) be the Bergman kernel function of Ω. Then there exist two positive constants m and M, and a function F such thatholds for every Z∈Ω . Hereand is the defining function of Ω The constants m and M depend only on Ω = This result extends some previous known results.展开更多
In this paper, we compute the Bergman kernel function on WIII.and RIII(q) denote the Cartan domain of the third class. Because domain WIII is neither homogeneous domain nor Reinhardt domain, we will use a new way to s...In this paper, we compute the Bergman kernel function on WIII.and RIII(q) denote the Cartan domain of the third class. Because domain WIII is neither homogeneous domain nor Reinhardt domain, we will use a new way to solve this problem. First, we give a holomorphic automorphism group, such that for any Zo, there exists an element of this group, which maps (W, Zo) into (W,O). Second, introduce the concept of semi-Reinhardt and discuss the complete orthonormal system of this domain.展开更多
文摘In this paper, we give an explicit formula of the Bergman kernel function on Hua Construction of the second type when the parameters 1/p1,…, 1/pr-1 are positive integers and 1/pr is an arbitrary positive real number.
基金supported by the National Natural Science Foundation of China(No.11871044)the Natural Science Foundation of Hebei Province(No.A2019106037)
文摘The authors give the condition that the Bergman kernel function on the first type of Cartan-Hartogs domain exists zeros.If the Bergman kernel function of this type of domain has zeros,the zero set is composed of several path-connected branches,and there exists a continuous curve to connect any two points in the non-zero set.
文摘The boundary behavior of the Bergman kernel function of a kind of Reinhardt domain is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points ( Z, Z) Let Q be the Reinhardt domainwhere is the Standard Euclidean norm in and let K( Z, W) be the Bergman kernel function of Ω. Then there exist two positive constants m and M, and a function F such thatholds for every Z∈Ω . Hereand is the defining function of Ω The constants m and M depend only on Ω = This result extends some previous known results.
基金Supported by the NSFC（10771144 11071171） Supported by the Beijing Natural Science Foundation（1082005） Supported by the Excellent Doctoral Thesis Prize of Beijing（2008）
文摘We obtain the Bergman kernel for a new type of Hartogs domain.The corresponding LU Qi-Keng's problem is considered.
文摘In this paper, we compute the Bergman kernel function on WIII.and RIII(q) denote the Cartan domain of the third class. Because domain WIII is neither homogeneous domain nor Reinhardt domain, we will use a new way to solve this problem. First, we give a holomorphic automorphism group, such that for any Zo, there exists an element of this group, which maps (W, Zo) into (W,O). Second, introduce the concept of semi-Reinhardt and discuss the complete orthonormal system of this domain.
