共查询到20条相似文献,搜索用时 46 毫秒
1.
J. K. Langley 《Proceedings of the American Mathematical Society》2007,135(9):2821-2826
Let be a convex domain in . Let be summable constants and let . If the converge sufficiently rapidly to from within an appropriate Stolz angle, then the function has infinitely many zeros in . An example shows that the hypotheses on the are not redundant and that two recently advanced conjectures are false.
2.
Mihai Mihailescu Vicentiu Radulescu 《Proceedings of the American Mathematical Society》2007,135(9):2929-2937
We consider the nonlinear eigenvalue problem in , on , where is a bounded open set in with smooth boundary and , are continuous functions on such that , , and for all . The main result of this paper establishes that any sufficiently small is an eigenvalue of the above nonhomogeneous quasilinear problem. The proof relies on simple variational arguments based on Ekeland's variational principle.
3.
Jorge Garcí a-Meliá n 《Proceedings of the American Mathematical Society》2007,135(9):2785-2793
In this paper, we prove that for the problem in a bounded domain of has a unique positive solution with on . The nonnegative weight is continuous in , but is only assumed to verify a ``bounded oscillations" condition of local nature near , in contrast with previous works, where a definite behavior of near was imposed.
4.
Let be a finite system of residue classes which forms an -cover of (i.e., every integer belongs to at least members of ). In this paper we show the following sharp result: For any positive integers and , if there is such that the fractional part of is , then there are at least such subsets of . This extends an earlier result of M. Z. Zhang and an extension by Z. W. Sun. Also, we generalize the above result to -covers of the integral ring of any algebraic number field with a power integral basis.
5.
B. P. Duggal 《Proceedings of the American Mathematical Society》2007,135(9):2899-2905
A Banach space operator is completely hereditarily normaloid, , if either every part, and (also) for every invertible part , of is normaloid or if for every complex number every part of is normaloid. Sufficient conditions for the perturbation of by an algebraic operator to satisfy Weyl's theorem are proved. Our sufficient conditions lead us to the conclusion that the conjugate operator satisfies -Weyl's theorem.
6.
Let and be compact Hausdorff spaces, be a Banach lattice and be an AM space with unit. Let be a Riesz isomorphism such that if and only if for each . We prove that is homeomorphic to and is Riesz isomorphic to . This generalizes some known results.
7.
Nicholas Proudfoot 《Proceedings of the American Mathematical Society》2007,135(12):3989-3994
Given a hyperplane arrangement in a real vector space , we introduce a real algebraic prevariety , and exhibit the complement of in the complexification of as the total space of an affine bundle over with fibers modeled on the dual vector space .
8.
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.
9.
Marian Nowak 《Proceedings of the American Mathematical Society》2007,135(9):2803-2809
Let be an ideal of over a -finite measure space , and let stand for the order dual of . For a real Banach space let be a subspace of the space of -equivalence classes of strongly -measurable functions and consisting of all those for which the scalar function belongs to . For a real Banach space a linear operator is said to be order-weakly compact whenever for each the set is relatively weakly compact in . In this paper we examine order-weakly compact operators . We give a characterization of an order-weakly compact operator in terms of the continuity of the conjugate operator of with respect to some weak topologies. It is shown that if is an order continuous Banach function space, is a Banach space containing no isomorphic copy of and is a weakly sequentially complete Banach space, then every continuous linear operator is order-weakly compact. Moreover, it is proved that if is a Banach function space, then for every Banach space any continuous linear operator is order-weakly compact iff the norm is order continuous and is reflexive. In particular, for every Banach space any continuous linear operator is order-weakly compact iff is reflexive.
10.
Helge Glö ckner Lutz G. Lucht Stefan Porubsky 《Proceedings of the American Mathematical Society》2007,135(6):1619-1629
In the -algebra of arithmetic functions , endowed with the usual pointwise linear operations and the Dirichlet convolution, let denote the convolution power with factors . We investigate the solvability of polynomial equations of the form with fixed coefficients . In some cases the solutions have specific properties and can be determined explicitly. We show that the property of the coefficients to belong to convergent Dirichlet series transfers to those solutions , whose values are simple zeros of the polynomial . We extend this to systems of convolution equations, which need not be of polynomial-type.
11.
Andreas Weingartner 《Proceedings of the American Mathematical Society》2007,135(9):2677-2681
Let be the sum of the positive divisors of . We show that the natural density of the set of integers satisfying is given by , where denotes Euler's constant. The same result holds when is replaced by , where is Euler's totient function.
12.
Let or , where is the algebra of a bounded linear operator acting on the Hilbert space , and is the set of self-adjoint operators in . Denote the numerical range of by It is shown that a surjective map satisfies if and only if there is a unitary operator such that has the form where is the transpose of with respect to a fixed orthonormal basis. In other words, the map or is a -isomorphism on and a Jordan isomorphism on . Moreover, if has finite dimension, then the surjective assumption on can be removed.
13.
Reza Sazeedeh 《Proceedings of the American Mathematical Society》2007,135(8):2339-2345
Let be a Noetherian homogeneous ring with local base ring and let be a finitely generated graded -module. Let be the largest integer such that is not Artinian. We will prove that are Artinian for all and there exists a polynomial of degree less than such that for all . Let be the first integer such that the local cohomology module is not cofinite. We will show that for all the graded module is Artinian.
14.
Esteban Andruchow Lá zaro Recht Alejandro Varela 《Proceedings of the American Mathematical Society》2007,135(8):2527-2537
We consider the problem of finding short smooth curves of isometries in a Hilbert space . The length of a smooth curve , , is measured by means of , where denotes the usual norm of operators. The initial value problem is solved: for any isometry and each tangent vector at (which is an operator of the form with ) with norm less than or equal to , there exist curves of the form , with initial velocity , which are short along their path. These curves, which we call metric geodesics, need not be unique, and correspond to the so called extension problem considered by M.G. Krein and others: in our context, given a symmetric operator find all possible extending to all , with . We also consider the problem of finding metric geodesics joining two given isometries and . It is well known that if there exists a continuous path joining and , then both ranges have the same codimension. We show that if this number is finite, then there exist metric geodesics joining and .
15.
G. Bouchitté C. Jimenez M. Rajesh 《Proceedings of the American Mathematical Society》2007,135(11):3525-3535
Let be a bounded Lipschitz regular open subset of and let be two probablity measures on . It is well known that if is absolutely continuous, then there exists, for every , a unique transport map pushing forward on and which realizes the Monge-Kantorovich distance . In this paper, we establish an bound for the displacement map which depends only on , on the shape of and on the essential infimum of the density .
16.
Pietro Poggi-Corradini 《Proceedings of the American Mathematical Society》2007,135(9):2893-2898
There is a universal constant with the following property. Suppose that is an analytic function on the unit disk , and suppose that there exists a constant so that the Euclidean area, counting multiplicity, of the portion of which lies over the disk , centered at and of radius , is strictly less than the area of . Then must send into . This answers a conjecture of Don Marshall.
17.
Maria Fernanda Elbert Barbara Nelli Harold Rosenberg 《Proceedings of the American Mathematical Society》2007,135(10):3359-3366
Let be a Riemannian manifold with sectional curvatures uniformly bounded from below. When we prove that there are no complete (strongly) stable -hypersurfaces, without boundary, provided is large enough. In particular, we prove that there are no complete strongly stable -hypersurfaces in without boundary,
18.
Constantin Costara Thomas Ransford 《Proceedings of the American Mathematical Society》2007,135(9):2779-2784
Let be the algebra of complex matrices, and for denote by and the spectrum and spectral radius of respectively. Let be a domain in containing 0, and let be a holomorphic map. We prove: (1) if for , then for ; (2) if for , then again for . Both results are special cases of theorems expressing the irreducibility of the spectrum near .
19.
Piotr Kot 《Proceedings of the American Mathematical Society》2007,135(12):3895-3903
We consider a circular, bounded, strictly convex domain with boundary of class . For any compact subset of we construct a sequence of homogeneous polynomials on which are big at each point of . As an application for any circular subset of type we construct a holomorphic function which is square integrable on and such that where denotes unit disc in .
20.
Let be a compact metric space and let be a real number with The aim of this paper is to solve a linear preserver problem on the Banach algebra of Hölder functions of order from into We show that each linear bijection having the property that for every where is of the form for every where with is a surjective isometry and is a linear functional.