共查询到10条相似文献，搜索用时 93 毫秒
1.
Nakao Hayashi Pavel I. Naumkin Yasuko Yamazaki 《Proceedings of the American Mathematical Society》2002,130(3):779-789
We consider the derivative nonlinear Schrödinger equations
where the coefficient satisfies the time growth condition
is a sufficiently small constant and the nonlinear interaction term consists of cubic nonlinearities of derivative type
where and . We suppose that the initial data satifsfy the exponential decay conditions. Then we prove the sharp decay estimate , for all , where . Furthermore we show that for there exist the usual scattering states, when and the modified scattering states, when
where the coefficient satisfies the time growth condition
is a sufficiently small constant and the nonlinear interaction term consists of cubic nonlinearities of derivative type
where and . We suppose that the initial data satifsfy the exponential decay conditions. Then we prove the sharp decay estimate , for all , where . Furthermore we show that for there exist the usual scattering states, when and the modified scattering states, when
2.
Tewodros Amdeberhan Olivier Espinosa Victor H. Moll 《Proceedings of the American Mathematical Society》2008,136(9):3211-3221
The definite integral is related to the Laplace transform of the digamma function by when . Certain analytic expressions for in the complementary range, , are also provided.
3.
Mayte Pé rez-Llanos Julio D. Rossi 《Proceedings of the American Mathematical Society》2008,136(2):593-596
We provide examples of solutions to parabolic problems with nontrivial blow-up sets of dimension strictly smaller than the space dimension. To this end we just consider different diffusion operators in different variables, for example, or . For both equations, we prove that there exists a solution that blows up in the segment .
4.
, 
, and its application to determinate moment problems Andrew G. Bakan 《Proceedings of the American Mathematical Society》2008,136(10):3579-3589
It has been proved that algebraic polynomials are dense in the space , , iff the measure is representable as with a finite non-negative Borel measure and an upper semi-continuous function such that is a dense subset of the space as equipped with the seminorm . The similar representation ( ) with the same and ( , and is also a dense
subset of ) corresponds to all those measures (supported by ) that are uniquely determined by their moments on ( ). The proof is based on de Branges' theorem (1959) on weighted polynomial approximation. A more general question on polynomial denseness in a separable Fréchet space in the sense of Banach has also been examined.
5.
Yun-Guang Lu 《Proceedings of the American Mathematical Society》2002,130(12):3579-3583
This paper is concerned with a nonlinear system which arises in chromatography. The global existence of solutions in space for a Cauchy problem with initial data is obtained for any fixed 0$">, and the convergence of to its equilibrium state , governed by a limit system is proved for the case by using the compensated compactness coupled with the framework of Tzavaras (1999).
6.
-Laplacian Arkady Poliakovsky Itai Shafrir 《Proceedings of the American Mathematical Society》2005,133(9):2549-2557
We study existence and uniqueness of positive eigenfunctions for the singular eigenvalue problem: on a bounded smooth domain with zero boundary condition. We also characterize all positive solutions of in .
7.
Olivera Djordjevic Miroslav Pavlovic 《Proceedings of the American Mathematical Society》2007,135(11):3607-3611
The following is proved: If is a function harmonic in the unit ball and if then the inequality holds, where is the nontangential maximal function of This improves a recent result of Stoll. This inequality holds for polyharmonic and hyperbolically harmonic functions as well.
8.
B. P. Duggal 《Proceedings of the American Mathematical Society》2006,134(6):1727-1734
Let denote the algebra of operators on a Hilbert . If and are commuting normal operators, and and are commuting quasi-nilpotents such that , then define and by , , and . It is proved that and , where is some scalar and is the quasi-nilpotent part of the operator .
9.
M. Barraa 《Proceedings of the American Mathematical Society》2005,133(6):1723-1726
Let and denote two -tuples of operators with and Let denote the elementary operators defined on the Hilbert-Schmidt class by We show that
Here is the essential numerical range, is the joint numerical range and is the joint essential numerical range.
Here is the essential numerical range, is the joint numerical range and is the joint essential numerical range.
10.
Let be a weight sequence of positive real numbers and let be a subnormal weighted shift with a weight sequence . Consider an extended weight sequence with and let 0: W_{\alpha (x)} \text{is} k \text{-hyponormal}\}$">for , where is the set of natural numbers. We obtain a formula to find the interval , which provides several examples to distinguish the classes of -hyponormal operators from one another.