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
The average σ-K width of the Sobolev-Wiener class in Lq(Rn) is studied for and the asymptotic behaviour of this quantity is determined. The exact value of average σ-K width of some class of smooth functions in L2(Rn...The average σ-K width of the Sobolev-Wiener class in Lq(Rn) is studied for and the asymptotic behaviour of this quantity is determined. The exact value of average σ-K width of some class of smooth functions in L2(Rn) is obtained.展开更多
Abstract This paper deals with the relationship between the positivity of the Fock Toeplitz operators and their Berezin transforms. The author considers the special case of the bounded radial function φ(z)=α + be...Abstract This paper deals with the relationship between the positivity of the Fock Toeplitz operators and their Berezin transforms. The author considers the special case of the bounded radial function φ(z)=α + be-α|z|2 + ce-β|z|2, where a, b, c are real numbers and α,β are positive numbers. For this type of φ, one can choose these parameters such that the Berezin transform of is a nonnegative function on the complex plane, but the corresponding Toeplitz operator Tφ is not positive on the Fock space.展开更多
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.
文摘The average σ-K width of the Sobolev-Wiener class in Lq(Rn) is studied for and the asymptotic behaviour of this quantity is determined. The exact value of average σ-K width of some class of smooth functions in L2(Rn) is obtained.
基金supported by the Chongqing Natural Science Foundation of China(No.cstc 2013jj B0050)
文摘Abstract This paper deals with the relationship between the positivity of the Fock Toeplitz operators and their Berezin transforms. The author considers the special case of the bounded radial function φ(z)=α + be-α|z|2 + ce-β|z|2, where a, b, c are real numbers and α,β are positive numbers. For this type of φ, one can choose these parameters such that the Berezin transform of is a nonnegative function on the complex plane, but the corresponding Toeplitz operator Tφ is not positive on the Fock space.