The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Ta...The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2＋ .展开更多
Let K ∈ L1(R) and let f ∈ L∞(R) be two functions on R.The convolution(Kf)(x) =∫R K(x-y)f(y)dy can be considered as an average of f with weight defined by K.Wiener's Tauberian theorem says that under suitable c...Let K ∈ L1(R) and let f ∈ L∞(R) be two functions on R.The convolution(Kf)(x) =∫R K(x-y)f(y)dy can be considered as an average of f with weight defined by K.Wiener's Tauberian theorem says that under suitable conditions,if lim x→∞(K f)(x) = lim x→∞(K A)(x) for some constant A,then lim x→∞ f(x) = A.We prove the following-adic analogue of this theorem:Suppose K,F,G are perverse-adic sheaves on the affine line A over an algebraically closed field of characteristic p(p=l).Under suitable conditions,if(K F)|η∞≌(K G)|η∞,then F|η∞≌ G|η∞,where η∞ is the spectrum of the local field of A at ∞.展开更多
This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts servi...This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts serving, it serves all customers in the queue in a single batch, which is the so-called batch service. If a new customer or a retrial customer finds all the customers’ rooms are occupied, he will decide whether or not to join the retrial orbit. By using the censoring technique and the matrix analysis method, we first obtain the decay function of the stationary distribution for the quantity of customers in the retrial orbit and the quantity of customers in the queue. Then based on the form of decay rate function and the Karamata Tauberian theorem, we finally get the exact tail asymptotics of the stationary distribution.展开更多
The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros has been recently generalized onto subharmonic functions with the Riesz measure on a half-line in Rn, n≥3. Here we extend ...The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros has been recently generalized onto subharmonic functions with the Riesz measure on a half-line in Rn, n≥3. Here we extend the Drasin complement to the Valiron-Titchmarsh theorem and show that if u is a subharmonic function of this class and of order 0〈ρ〈1, then the existence of the limit limr→∞logu（r）/N（r）, where N（r） is the integrated counting function of the masses of u, implies the regular asymptotic behavior for both u and its associated measure.展开更多
文摘The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2＋ .
基金supported by National Natural Science Foundation of China (Grant No.10525107)
文摘Let K ∈ L1(R) and let f ∈ L∞(R) be two functions on R.The convolution(Kf)(x) =∫R K(x-y)f(y)dy can be considered as an average of f with weight defined by K.Wiener's Tauberian theorem says that under suitable conditions,if lim x→∞(K f)(x) = lim x→∞(K A)(x) for some constant A,then lim x→∞ f(x) = A.We prove the following-adic analogue of this theorem:Suppose K,F,G are perverse-adic sheaves on the affine line A over an algebraically closed field of characteristic p(p=l).Under suitable conditions,if(K F)|η∞≌(K G)|η∞,then F|η∞≌ G|η∞,where η∞ is the spectrum of the local field of A at ∞.
文摘This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts serving, it serves all customers in the queue in a single batch, which is the so-called batch service. If a new customer or a retrial customer finds all the customers’ rooms are occupied, he will decide whether or not to join the retrial orbit. By using the censoring technique and the matrix analysis method, we first obtain the decay function of the stationary distribution for the quantity of customers in the retrial orbit and the quantity of customers in the queue. Then based on the form of decay rate function and the Karamata Tauberian theorem, we finally get the exact tail asymptotics of the stationary distribution.
文摘The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros has been recently generalized onto subharmonic functions with the Riesz measure on a half-line in Rn, n≥3. Here we extend the Drasin complement to the Valiron-Titchmarsh theorem and show that if u is a subharmonic function of this class and of order 0〈ρ〈1, then the existence of the limit limr→∞logu（r）/N（r）, where N（r） is the integrated counting function of the masses of u, implies the regular asymptotic behavior for both u and its associated measure.
