共查询到20条相似文献，搜索用时 31 毫秒
1.
Mitsuru Uchiyama 《Proceedings of the American Mathematical Society》2001,129(11):3339-3344
For bounded non-negative operators and , Furuta showed
We will extend this as follows: implies
where is a harmonic mean of and . The idea of the proof comes from Jensen's inequality for an operator convex function by Hansen-Pedersen.
2.
Philippe Poulin 《Proceedings of the American Mathematical Society》2007,135(1):77-85
It is well known that the Green function of the standard discrete Laplacian on , exhibits a pathological behavior in dimension . In particular, the estimate fails for . This fact complicates the study of the scattering theory of discrete Schrödinger operators. Molchanov and Vainberg suggested the following alternative to the standard discrete Laplacian, and conjectured that the estimate holds for all . In this paper we prove this conjecture.
3.
We prove that for integers 1,m\geq 1$"> and positive rationals the series
is irrational. Furthermore, if all the positive rationals are less than then the series
is also irrational.
is irrational. Furthermore, if all the positive rationals are less than then the series
is also irrational.
4.
Zhao established a curious harmonic congruence for prime : In this note the authors extend it to the following congruence for any prime and positive integer : Other improvements on congruences of harmonic sums are also obtained.
5.
Aleksandar Petojevic H. M. Srivastava 《Proceedings of the American Mathematical Society》2008,136(8):2719-2728
In this paper the authors present several algorithmic formulas which are potentially useful in computing the following Mordell-Tornheim zeta values: for the special cases
and
Some interesting (known or new) consequences and illustrative examples are also considered. 6.
Nakao Hayashi Elena I. Kaikina Pavel I. Naumkin 《Transactions of the American Mathematical Society》2006,358(3):1165-1185
We study large time asymptotics of small solutions to the Cauchy problem for nonlinear damped wave equations with a critical nonlinearity
where 0,$"> and space dimensions . Assume that the initial data
where \frac{n}{2},$"> weighted Sobolev spaces are
Also we suppose that
where
Then we prove that there exists a positive such that the Cauchy problem above has a unique global solution satisfying the time decay property
for all 0,$"> where
where 0,$"> and space dimensions . Assume that the initial data
where \frac{n}{2},$"> weighted Sobolev spaces are
Also we suppose that
0,\int u_{0}\left( x\right) dx>0, \end{displaymath}">
where
Then we prove that there exists a positive such that the Cauchy problem above has a unique global solution satisfying the time decay property
for all 0,$"> where
7.
David Benko Tamá s Erdé lyi Jó zsef Szabados 《Proceedings of the American Mathematical Society》2003,131(8):2385-2391
For a function defined on an interval let
The principal result of this paper is the following Markov-type inequality for Müntz polynomials. Theorem. Let be an integer. Let be distinct real numbers. Let . Then
where the supremum is taken for all (the span is the linear span over ).
The principal result of this paper is the following Markov-type inequality for Müntz polynomials. Theorem. Let be an integer. Let be distinct real numbers. Let . Then
where the supremum is taken for all (the span is the linear span over ).
8.
Natan Kruglyak Eric Setterqvist 《Proceedings of the American Mathematical Society》2008,136(7):2505-2513
It is shown that if we restrict the identity minus Hardy operator on the cone of nonnegative decreasing functions in , then we have the sharp estimate for In other words, for each and each integer . for all .
It is also shown, via a connection between the operator and Laguerre functions, that
9.
On a Liouville-type theorem and the Fujita blow-up phenomenon 总被引：3，自引：0，他引：3
The main purpose of this paper is to obtain the well-known results of H.Fujita and K.Hayakawa on the nonexistence of nontrivial nonnegative global solutions for the Cauchy problem for the equation
with on the half-space as a consequence of a new Liouville theorem of elliptic type for solutions of () on . This new result is in turn a consequence of other new phenomena established for nonlinear evolution problems. In particular, we prove that the inequality
has no nontrivial solutions on when We also show that the inequality
has no nontrivial nonnegative solutions for , and it has no solutions on bounded below by a positive constant for 1.$">
with on the half-space as a consequence of a new Liouville theorem of elliptic type for solutions of () on . This new result is in turn a consequence of other new phenomena established for nonlinear evolution problems. In particular, we prove that the inequality
has no nontrivial solutions on when We also show that the inequality
has no nontrivial nonnegative solutions for , and it has no solutions on bounded below by a positive constant for 1.$">
10.
The triple integrals
and
where and are complex variables in suitably defined cut planes, were first evaluated by Watson in 1939 for the special cases and , respectively. In the present paper simple direct methods are used to prove that can be expressed in terms of squares of complete elliptic integrals of the first kind for general values of and . It is also shown that and are related by the transformation formula
where
Thus both of Watson's results for are contained within a single formula for .
and
where and are complex variables in suitably defined cut planes, were first evaluated by Watson in 1939 for the special cases and , respectively. In the present paper simple direct methods are used to prove that can be expressed in terms of squares of complete elliptic integrals of the first kind for general values of and . It is also shown that and are related by the transformation formula
where
Thus both of Watson's results for are contained within a single formula for .
11.
Andrá s Domokos Juan J. Manfredi 《Proceedings of the American Mathematical Society》2005,133(4):1047-1056
We prove Cordes type estimates for subelliptic linear partial differential operators in non-divergence form with measurable coefficients in the Heisenberg group. As an application we establish interior horizontal -regularity for p-harmonic functions in the Heisenberg group for the range .
12.
Oliver Roth 《Proceedings of the American Mathematical Society》2007,135(7):2051-2054
We prove the sharp inequality for the logarithmic coefficients of a normalized univalent function in the unit disk.
13.
Horst Alzer 《Proceedings of the American Mathematical Society》2007,135(11):3641-3648
Let and be real numbers. The inequality holds for all positive real numbers if and only if . The reverse inequality is valid for all if and only if .
14.
Norimichi Hirano Naoki Shioji 《Proceedings of the American Mathematical Society》2006,134(9):2585-2592
Let , let and let be a bounded domain with a smooth boundary . Our purpose in this paper is to consider the existence of solutions of the problem: where
15.
Aurel Spataru 《Proceedings of the American Mathematical Society》2004,132(11):3387-3395
Let be i.i.d. random variables with , and set . We prove that, for
under the assumption that and Necessary and sufficient conditions for the convergence of the sum above were established by Lai (1974).
under the assumption that and Necessary and sufficient conditions for the convergence of the sum above were established by Lai (1974).
16.
-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 .
17.
Chunlei Liu 《Proceedings of the American Mathematical Society》2002,130(7):1887-1892
Let be a nontrivial Dirichlet character modulo an odd prime . Write
We shall prove
and, for complex ,
where is a constant depending only on .
We shall prove
and, for complex ,
0, \end{displaymath}">
where is a constant depending only on .
18.
Raú l E. Curto Il Bong Jung Woo Young Lee 《Proceedings of the American Mathematical Society》2002,130(2):565-576
Given an -step extension of a recursively generated weight sequence , and if denotes the associated unilateral weighted shift, we prove that
In particular, the subnormality of an extension of a recursively generated weighted shift is independent of its length if the length is bigger than 1. As a consequence we see that if is a canonical rank-one perturbation of the recursive weight sequence , then subnormality and -hyponormality for eventually coincide. We then examine a converse--an ``extremality" problem: Let be a canonical rank-one perturbation of a weight sequence and assume that -hyponormality and -hyponormality for coincide. We show that is recursively generated, i.e., is recursive subnormal.
1).\end{cases}\end{displaymath}">
In particular, the subnormality of an extension of a recursively generated weighted shift is independent of its length if the length is bigger than 1. As a consequence we see that if is a canonical rank-one perturbation of the recursive weight sequence , then subnormality and -hyponormality for eventually coincide. We then examine a converse--an ``extremality" problem: Let be a canonical rank-one perturbation of a weight sequence and assume that -hyponormality and -hyponormality for coincide. We show that is recursively generated, i.e., is recursive subnormal.
19.
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
20.
Finbarr Holland 《Proceedings of the American Mathematical Society》2007,135(9):2915-2920
As a consequence of a more general statement proved in the paper, it is deduced that, if , and , then with equality if and only if . This is a new refinement of Carleman's classic inequality.