In this paper,the author study the spectrum of high rank differential operators T (n) (t) of C 0 Semigroup T(t) ,given an approach to construct the spectral set opetator T (n) (t) ,and discussed the relat...In this paper,the author study the spectrum of high rank differential operators T (n) (t) of C 0 Semigroup T(t) ,given an approach to construct the spectral set opetator T (n) (t) ,and discussed the relation between the spectral points of both T (n) (t) and infinitesimal generator A of T(t) .展开更多
In this paper,the author study the spectrum of high rank differential operators T (n) (t) of C 0 Semigroup T(t) ,given an approach to construct the spectral set opetator T (n) (t) ,and discussed the relat...In this paper,the author study the spectrum of high rank differential operators T (n) (t) of C 0 Semigroup T(t) ,given an approach to construct the spectral set opetator T (n) (t) ,and discussed the relation between the spectral points of both T (n) (t) and infinitesimal generator A of T(t) .展开更多
The determinant representation of the gauge transformation operators is establised. In this process, the generalized Wronskian determinant is introduced. As a simple application, the authors present a construction of ...The determinant representation of the gauge transformation operators is establised. In this process, the generalized Wronskian determinant is introduced. As a simple application, the authors present a construction of the special T-function obtained firstly by Chau et al. (Commun. Math. Phys., 149(1992), 263), which involves the generalized Wronskian determinant. Also, some properties of this determinant are given.展开更多
In this paper,a sufficient and necessary condition is obtained to ensure that the spectrum of a class of 2n-order weighted differential operators is discrete.The proof is based on the method of certain weighted Sobole...In this paper,a sufficient and necessary condition is obtained to ensure that the spectrum of a class of 2n-order weighted differential operators is discrete.The proof is based on the method of certain weighted Sobolev spaces to be compactly embedded in weighted L^2(R).展开更多
This paper continues the studies of the essential spectrum Of nonsemi-bounded pseudodifferential operators. The author improves the results in [5] in some sense. For the relativisticSchredinger operator, ￣ + v(x), co...This paper continues the studies of the essential spectrum Of nonsemi-bounded pseudodifferential operators. The author improves the results in [5] in some sense. For the relativisticSchredinger operator, ￣ + v(x), complete results are obtained.展开更多
文摘In this paper,the author study the spectrum of high rank differential operators T (n) (t) of C 0 Semigroup T(t) ,given an approach to construct the spectral set opetator T (n) (t) ,and discussed the relation between the spectral points of both T (n) (t) and infinitesimal generator A of T(t) .
文摘In this paper,the author study the spectrum of high rank differential operators T (n) (t) of C 0 Semigroup T(t) ,given an approach to construct the spectral set opetator T (n) (t) ,and discussed the relation between the spectral points of both T (n) (t) and infinitesimal generator A of T(t) .
基金Project supported by the State Education Commission, the 973 Project "Nonlinear Science" the National Natural Science Foundation of China (No.9725104, No.19971084).
文摘The determinant representation of the gauge transformation operators is establised. In this process, the generalized Wronskian determinant is introduced. As a simple application, the authors present a construction of the special T-function obtained firstly by Chau et al. (Commun. Math. Phys., 149(1992), 263), which involves the generalized Wronskian determinant. Also, some properties of this determinant are given.
基金This research is supported by the National Natural Science Foundation of China(No.10071048).
文摘In this paper,a sufficient and necessary condition is obtained to ensure that the spectrum of a class of 2n-order weighted differential operators is discrete.The proof is based on the method of certain weighted Sobolev spaces to be compactly embedded in weighted L^2(R).
文摘This paper continues the studies of the essential spectrum Of nonsemi-bounded pseudodifferential operators. The author improves the results in [5] in some sense. For the relativisticSchredinger operator, ￣ + v(x), complete results are obtained.
