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1.
S. Prashanth 《Proceedings of the American Mathematical Society》2007,135(1):201-209
Let denote the closure of in the norm Let and define the constants and Let We consider the following problem for We show an exact multiplicity result for for all small .
2.
Sheng Wang Wang 《Proceedings of the American Mathematical Society》2002,130(11):3355-3367
This paper introduces the concept of Hille-Yosida operators and studies several generation theorems. We show that if a once-integrated semigroup satisfies for all 0 a. e.$">, then is locally bounded on and exponentially bounded. In addition, some other interesting results are presented.
3.
Let and be relatively prime monic irreducible polynomials in (). In this paper, we give an elementary proof for the following law of quadratic reciprocity in : where is the Legendre symbol.
4.
G. Paouris 《Proceedings of the American Mathematical Society》2005,133(2):565-575
We discuss the following question: Do there exist an absolute constant 0$"> and a sequence tending to infinity with , such that for every isotropic convex body in and every the inequality holds true? Under the additional assumption that is 1-unconditional, Bobkov and Nazarov have proved that this is true with . The question is related to the central limit properties of isotropic convex bodies. Consider the spherical average . We prove that for every and every isotropic convex body in , the statements (A) ``for every , " and (B) ``for every , , where " are equivalent.
5.
The algebra of unbounded holomorphic functions that is contained in the algebra is studied. For in but not in , we show that the algebra generated by and is dense in for all .
6.
Emmanuel Montini 《Transactions of the American Mathematical Society》2003,355(4):1415-1441
In this article, we study the pointwise convergence of the spherical partial integral operator when it is applied to functions with a certain amount of smoothness. In particular, for , , , we prove that -quasieverywhere on , where is such that almost everywhere. A weaker version of this result in the range as well as some related localisation principles are also obtained. For and , we construct a function such that diverges everywhere.
7.
We consider an invertible operator on a Banach space whose spectrum is an interpolating set for Hölder classes. We show that if , , with and , then for all , assuming that satisfies suitable regularity conditions. When is a Hilbert space and (i.e. is a contraction), we show that under the same assumptions, is unitary and this is sharp.
8.
Consecutive numbers with the same Legendre symbol 总被引:1,自引:0,他引:1
Zhi-Hong Sun 《Proceedings of the American Mathematical Society》2002,130(9):2503-2507
Let be an odd prime, and be a complete set of residues . The goal of the paper is to determine all the values of such that or , where is the Legendre symbol.
9.
Tamá s Erdé lyi 《Proceedings of the American Mathematical Society》2003,131(10):3129-3134
Let be a set of distinct positive numbers. The span of
over will be denoted by
Our main result of this note is the following.
over will be denoted by
Our main result of this note is the following.
Theorem. Suppose . Let be a non-negative integer. Then there are constants 0$"> and 0$"> depending only on , , and such that
where the lower bound holds for all and for all , while the upper bound holds when and and when , , and .
10.
Adam Osekowski 《Proceedings of the American Mathematical Society》2008,136(8):2951-2958
Let be a nonnegative supermartingale and be a predictable process with values in . Let denote the stochastic integral of with respect to . The paper contains the proof of the sharp inequality where . A discrete-time version of this inequality is also established.
11.
Yves Fé lix Jean-Claude Thomas 《Proceedings of the American Mathematical Society》2004,132(1):305-312
Let be a simply-connected closed oriented -dimensional manifold. We prove that for any field of coefficients there exists a natural homomorphism of commutative graded algebras where is the loop algebra defined by Chas and Sullivan. As usual denotes the monoid of self-equivalences homotopic to the identity, and the space of based loops. When is of characteristic zero, yields isomorphisms where denotes the Hodge decomposition on .
12.
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.$">
with on the half-space as a consequence of a new Liouville theorem of elliptic type for solutions of () on . This new result is in turn a consequence of other new phenomena established for nonlinear evolution problems. In particular, we prove that the inequality
has no nontrivial solutions on when We also show that the inequality
has no nontrivial nonnegative solutions for , and it has no solutions on bounded below by a positive constant for 1.$">
13.
Abdelmalek Azizi 《Proceedings of the American Mathematical Society》2002,130(8):2197-2202
Let and be prime numbers such that and . Let , , and let be the 2-Hilbert class field of , the 2-Hilbert class field of and the Galois group of . The 2-part of the class group of is of type , so contains three extensions . Our goal is to study the problem of capitulation of the 2-classes of in , and to determine the structure of .
RS
14.
Let be the standard closed positive cone in and let be the set of integers for which there exists a continuous, order preserving, subhomogeneous map , which has a periodic point with period . It has been shown by Akian, Gaubert, Lemmens, and Nussbaum that is contained in the set consisting of those for which there exist integers and such that , , and for some . This note shows that for all .
15.
Kazuhiro Kuwae 《Proceedings of the American Mathematical Society》2004,132(9):2743-2751
We show the conservativeness of the Girsanov transformed diffusion process by drift with or 4d/(d+2)$">, or if is of the Hardy class with sufficiently small coefficient of energy . Here 0$"> is the lower bound of the symmetric measurable matrix-valued function appearing in the given Dirichlet form. In particular, our result improves the conservativeness of the transformed process by when .
16.
Gangsong Leng Lin Si Qingsan Zhu 《Proceedings of the American Mathematical Society》2004,132(9):2655-2660
For let and denote the arithmetic mean and geometric mean of elements of , respectively. It is proved that if is an integer in , then
with equality if and only if . Furthermore, as a generalization of this inequality, a mixed power-mean inequality for subsets is established.
with equality if and only if . Furthermore, as a generalization of this inequality, a mixed power-mean inequality for subsets is established.
17.
Let , , be a bounded smooth connected open set and be a map satisfying the hypotheses (H1)-(H4) below. Let with , in and with be two weak solutions of
Suppose that in . Then we show that u_1$"> in under the following assumptions: either u_1$"> on , or on and in . We also show a measure-theoretic version of the Strong Comparison Principle.
Suppose that in . Then we show that u_1$"> in under the following assumptions: either u_1$"> on , or on and in . We also show a measure-theoretic version of the Strong Comparison Principle.
18.
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
19.
Fang Gensun 《Proceedings of the American Mathematical Society》2000,128(9):2597-2601
Let be the discrete Hardy space, consisting of those sequences , such that , where , , is the discrete Hilbert transform of . For a sequence , let be the unique cardinal spline of degree interpolating to at the integers. The norm of this operator, , is called a Lebesgue constant from to , and it was proved that .
It is proved in this paper that
20.
Let be an ideal in a Noetherian local ring . Then the sequence is -regular if every is a non-zerodivisor in and if for all integers , where runs over the elements of the set .