In this note we deal with a class of holomorphic maps with generalized positive real part on Hilbert space. The distortion theorem and Pick Julia type theorem for these maps are obtained.
The authors give two cohomology vanishing theorems for domains, which are not pseudoconvex, and characterize the holomorphy of domains with smooth boundaries in separable Hilbert spaces through cohomology vanishing.
By using the index theory for linear bounded self-adjoint operators in a Hilbert space related to a fixed self-adjoint operator A with compact resolvent,the authors discuss the existence and multiplicity of solutions ...By using the index theory for linear bounded self-adjoint operators in a Hilbert space related to a fixed self-adjoint operator A with compact resolvent,the authors discuss the existence and multiplicity of solutions for(nonlinear) operator equations,and give some applications to some boundary value problems of first order Hamiltonian systems and second order Hamiltonian systems.展开更多
文摘In this note we deal with a class of holomorphic maps with generalized positive real part on Hilbert space. The distortion theorem and Pick Julia type theorem for these maps are obtained.
基金Korea Research Foundation Grant (KRF-2001-015-DP0015).
文摘The authors give two cohomology vanishing theorems for domains, which are not pseudoconvex, and characterize the holomorphy of domains with smooth boundaries in separable Hilbert spaces through cohomology vanishing.
基金Project supported by the National Natural Science Foundation of China (Nos.11071127,10621101,10901118)the 973 project of the Ministry of Science and Technology of China (No.2011CB808002)
文摘By using the index theory for linear bounded self-adjoint operators in a Hilbert space related to a fixed self-adjoint operator A with compact resolvent,the authors discuss the existence and multiplicity of solutions for(nonlinear) operator equations,and give some applications to some boundary value problems of first order Hamiltonian systems and second order Hamiltonian systems.
