In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theo...In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.展开更多
Dual actions with respect to U(1) gauge fields for the Born-Infeld and Dp-brane theories are reexamined.Taking into account an additional condition,i.e.a corollary to the field equation of the auxiliary metric,one obt...Dual actions with respect to U(1) gauge fields for the Born-Infeld and Dp-brane theories are reexamined.Taking into account an additional condition,i.e.a corollary to the field equation of the auxiliary metric,one obtainsan alternative dual action that does not involve the infinite series in the auxiliary metric given by [M.Abou Zeid andC.M.Hull,Phys.Lett.B 428 (1998) 277],but just picks out the first term from the series formally.New effectiveinteractions of the theories are revealed.That is,the new dual action gives rise to an effective interaction in terms ofone interaction term rather than infinitely many terms of different (higher) orders of interactions physically.However,the price paid for eliminating the infinite series is that the new action is not quadratic but highly nonlinear in the Hodgedual of a (p-1)-form field strength.This non-linearity is inevitable under the requirement that the two dual actionsare equivalent.展开更多
基金Supported by the Huazhong Agricultural University Scientific Technological Selfinnovation Foundation(2662014BQ058)the Fundamental Research Funds for the Central Universities(2662015QC010)the National Natural Science Foundation of China(11371156,11431007)
文摘In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.
基金Supported by the National Natural Science Foundation of China under Grant No.10675061the Doctoral Foundation of the Ministry of Education of China under Grant No.20060055006
文摘Dual actions with respect to U(1) gauge fields for the Born-Infeld and Dp-brane theories are reexamined.Taking into account an additional condition,i.e.a corollary to the field equation of the auxiliary metric,one obtainsan alternative dual action that does not involve the infinite series in the auxiliary metric given by [M.Abou Zeid andC.M.Hull,Phys.Lett.B 428 (1998) 277],but just picks out the first term from the series formally.New effectiveinteractions of the theories are revealed.That is,the new dual action gives rise to an effective interaction in terms ofone interaction term rather than infinitely many terms of different (higher) orders of interactions physically.However,the price paid for eliminating the infinite series is that the new action is not quadratic but highly nonlinear in the Hodgedual of a (p-1)-form field strength.This non-linearity is inevitable under the requirement that the two dual actionsare equivalent.
