共查询到20条相似文献,搜索用时 31 毫秒
1.
Application of the Trace Inequality to the Poisson Equation 总被引:1,自引:0,他引:1
Sadek Gala 《Positivity》2008,12(2):289-312
The purpose of this paper is to show that solutions of the Poisson equation
where f be a complex-valued distribution on , d ≥ 3 and satisfy the coercivity property : for all . The coercivity of this equation is well studied by Maz’ ya and Verbitsky [14] in the case where f belongs to the class of positive Borel measures.
相似文献
2.
Michael R. Darnel 《Algebra Universalis》2007,57(3):273-290
It is well known that the quasitorsion class of archimedean -groups is the class of -groups G such that every closed convex -subgroup is a polar, and it is also well known that the class of -groups G such that every convex -subgroup is a polar is a torsion class. By defining a selection on -groups, these two results are generalized to show, whenever and are selections on -groups, the class of -groups G such that is a radical class. Three selections in particular — all convex -subgroups, all polars, and all closed convex -subgroups — and the radical classes determined by them are studied in some detail.
Received March 7, 2006; accepted in final form August 29, 2006. 相似文献
3.
F. E. A. Johnson 《Archiv der Mathematik》2008,90(2):123-132
A module J over a ring is said to be hyperstable when . Over a module M for which Ext we show that the projective n-stems for which is hyperstable constitute a single homotopy type.
Received: 17 November 2006 相似文献
4.
Let be a convex function and be its Legendre tranform. It is proved that if is invariant by changes of signs, then . This is a functional version of the inverse Santaló inequality for unconditional convex bodies due to J. Saint Raymond.
The proof involves a general result on increasing functions on together with a functional form of Lozanovskii’s lemma. In the last section, we prove that for some c > 0, one has always . This generalizes a result of B. Klartag and V. Milman.
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5.
Lorenz J. Schwachhöfer 《Archiv der Mathematik》2008,90(2):158-162
We show that a left invariant metric on a compact Lie group G with Lie algebra has some negative sectional curvature if it is obtained by enlarging a biinvariant metric on a subalgebra , unless the semi-simple part of is an ideal of This answers a question raised in [8].
Received: 7 May 2007 相似文献
6.
Mikhail Kapranov 《Selecta Mathematica, New Series》2007,13(2):277-319
We construct algebraic and algebro-geometric models for the spaces of unparametrized paths. This is done by considering a
path as a holonomy functional on indeterminate connections. For a manifold X, we construct a Lie algebroid which serves as the tangent space to X (punctual paths) inside the space of all unparametrized paths. It serves as a natural receptacle of all “covariant derivatives
of the curvature” for all bundles with connections on X.
If X is an algebraic variety, we integrate to a formal groupoid which can be seen as the formal neighborhood of X inside the space of paths. We establish a relation between and the stable map spaces of Kontsevich.
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7.
Michel Weber 《Results in Mathematics》2007,51(1-2):141-179
Let where are independent Bernoulli random variables. In relation with the divisor problem, we evaluate the almost sure asymptotic
order of the sums , where and is a sequence of positive integers.
Received: May 23, 2007. Revised: June 8, 2007. 相似文献
8.
We define the reduced minimum modulus
of a nonzero element a in a unital C
*-algebra
by
. We prove that
. Applying this result to
and its closed two side ideal
, we get that dist
,
and
for any
if RR
= 0, where
and
is the quotient homomorphism and
. These results generalize corresponding results in Hilbert spaces. 相似文献
9.
We consider Dirichlet spaces (
) in L
2 and more general energy forms
in L
p
,
. For the latter we introduce the notions of an extended ’Dirichlet’ space and a transient form. Under the assumption that
, resp.
, are compactly embedded in L
2, resp. L
p
, we prove a Poincaré inequality for transient (Dirichlet) forms. If both
and its adjoint
are sub-Markovian semigroups, we show that the transience of T
t
is independent of
) and that it is implied by the transience of the energy form
of
and the form
belonging to
. 相似文献
10.
A set of positive integers is a perfect difference set if every nonzero integer has a unique representation as the difference of two elements of . We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach we prove that there exists a perfect difference set such that
.
Also we prove that there exists a perfect difference set
such that
A(x)/≥ 1/.
The work of J. C. was supported by Grant MTM 2005-04730 of MYCIT (Spain).
The work of M. B. N. was supported in part by grants from the NSA Mathematical Sciences Program and the PSC-CUNY Research
Award Program. 相似文献
11.
Amol Sasane 《Integral Equations and Operator Theory》2007,59(2):245-256
Let E, E* be separable Hilbert spaces. If S is an open subset of
, then
denotes the space of all functions
that are holomorphic in
, and bounded and continuous on
. In this article we prove the following results:
相似文献
1. | A theorem concerning the approximation of by a function F that is holomorphic in a neighbourhood of and such that the error F − f is uniformly bounded in the disk . |
2. | The corona theorem for when dim(E) < ∞: If there exists a δ > 0 such that for all , , then there exists a such that for all , g(z)f(z) = I. |
3. | The problem of complementing to an isomorphism for when {dim(E) < ∞ (Tolokonnikov’s lemma): has a left inverse iff it is a ‘part’ of an invertible element F in . |
12.
Zhongwei Tang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(5):810-833
In this paper, we are concerned with the multiplicity of standing wave solutions of nonlinear Schr?dinger equations with electromagnetic
fields
for sufficiently large λ, where i is the imaginary unit, for N ≥ 3 and 2 < p < + ∞ for N = 1, 2. a(x) is a real continuous function on is such that A
j
(x) is a real local H?lder continuous function on for j = 1, 2, ... ,N. We assume that a(x) is nonnegative and has a potential well consisting of k components . We show that for any non-empty subset has a standing wave solution which is trapped in a neighborhood of for λ large.
相似文献
13.
Morton E. Harris 《Results in Mathematics》2008,51(3-4):249-259
As in Finite Group Modular Representation Theory, let be a commutative complete noetherian ring with an algebraically closed residue field k. Let G be a finite group and let N be a normal subgroup of G. First suppose that V is an indecomposable -module, so that Inf
G
G/N
(V) is an indecomposable G-module. We relate the Green invariants of V as an -module to those of Inf
G
G/N
(V) as an G-module. Secondly, let V and W be indecomposable G-modules. Assume that W is an endo-permutation lattice and that is also an indecomposable G-module. We relate the Green invariants of the G-modules V and . (This situation arises under important Morita equivalences.)
Received: December 11, 2006. Revised: August 22, 2007. 相似文献
14.
S. Mecheri 《Journal of Mathematical Sciences》2000,102(5):4429-4435
A generalized derivation
, is defined by the formula
, where
and
is the Banach algebra of bounded linear operators in a Hilbert space
. Sufficient conditions under which
and
are given. Bibliography: 8 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 20, 2000, pp. 111–119. 相似文献
15.
Balanced pseudocomplemented Ockham algebras 总被引:1,自引:0,他引:1
16.
Attila Házy 《Aequationes Mathematicae》2007,74(3):210-218
Summary. A real-valued function f defined on an open convex set is called (d, t)-convex if it satisfies
for all , where is a given function and t
]0, 1[ is a fixed parameter.
The main result of the paper states that if f is locally bounded from above at a point of D and (d, t)-convex then it satisfies the convexity-type inequality (under some assumptions)
for all and s
[0, 1], where is defined as the fixed point of a certain contraction. The main result of this paper offers a generalization of the celebrated
Bernstein and Doetsch theorem and the recent results by Nikodem and Ng, Páles and the author.
This research was supported by the Hungarian Scientific Research Fund (OTKA) Grant T-038072 and K-62316. 相似文献
17.
Alejandra Maestripieri Francisco Martínez Pería 《Integral Equations and Operator Theory》2007,59(2):207-221
The aim of this work is to generalize the notions of Schur complements and shorted operators to Krein spaces. Given a (bounded)
J-selfadjoint operator A (with the unique factorization property) acting on a Krein space
and a suitable closed subspace
of
, the Schur complement
of A to
is defined. The basic properties of
are developed and different characterizations are given, most of them resembling those of the shorted of (bounded) positive
operators on a Hilbert space.
To the memory of Professor Mischa Cotlar 相似文献
18.
Let be a boolean function, and suppose that the spectral
norm
of f is at most M. Then where and each H
j
is a subgroup of . This result may be regarded as a quantitative analogue of the Cohen-Helson-Rudin structure theorem for idempotent measures
in locally compact abelian groups.
Received: May 2006 Accepted: January 2007 相似文献
19.
Let (V, g) be a Riemannian manifold and let be the isometric immersion operator which, to a map , associates the induced metric on V, where denotes the Euclidean scalar product in . By Nash–Gromov implicit function theorem is infinitesimally invertible over the space of free maps. In this paper we study non-free isometric immersions . We show that the operator (where denotes the space of C
∞- smooth quadratic forms on ) is infinitesimally invertible over a non-empty open subset of and therefore is an open map in the respective fine topologies.
相似文献
20.
Peter Bundschuh 《Results in Mathematics》2007,51(1-2):29-42
Let K be or an imaginary quadratic number field, and q
K an integer with |q| > 1. We give a quantitative version of the linear independence over K of the three numbers 1, , and an equivalent power series version. We also mention several open problems.
Received: February 5, 2007. Revised: April 18, 2007. 相似文献