共查询到20条相似文献,搜索用时 460 毫秒
1.
Glyn Harman 《Archiv der Mathematik》2008,90(3):239-245
Let P
+(m) denote the greatest prime factor of the positive integer m. Improving and simplifying work of Dartyge [3] we show that
for . Here improves on the previous exponent .
Received: 20 April 2007 相似文献
2.
Shahar Mendelson Alain Pajor Nicole Tomczak-Jaegermann 《Geometric And Functional Analysis》2007,17(4):1248-1282
We present a randomized method to approximate any vector from a set . The data one is given is the set T, vectors of and k scalar products , where are i.i.d. isotropic subgaussian random vectors in , and . We show that with high probability, any for which is close to the data vector will be a good approximation of , and that the degree of approximation is determined by a natural geometric parameter associated with the set T.
We also investigate a random method to identify exactly any vector which has a relatively short support using linear subgaussian
measurements as above. It turns out that our analysis, when applied to {−1, 1}-valued vectors with i.i.d. symmetric entries,
yields new information on the geometry of faces of a random {−1, 1}-polytope; we show that a k- dimensional random {−1, 1}-polytope with n vertices is m-neighborly for
The proofs are based on new estimates on the behavior of the empirical process when F is a subset of the L
2 sphere. The estimates are given in terms of the γ
2 functional with respect to the ψ
2 metric on F, and hold both in exponential probability and in expectation.
Received: November 2005, Revision: May 2006, Accepted: June 2006 相似文献
3.
Friedrich Haslinger 《Czechoslovak Mathematical Journal》2008,58(4):1247-1256
We prove that compactness of the canonical solution operator to restricted to (0, 1)-forms with holomorphic coefficients is equivalent to compactness of the commutator
defined on the whole L
(0,1)2(Ω), where is the multiplication by and is the orthogonal projection of L
(0,1)2(Ω) to the subspace of (0, 1) forms with holomorphic coefficients. Further we derive a formula for the -Neumann operator restricted to (0, 1) forms with holomorphic coefficients expressed by commutators of the Bergman projection
and the multiplications operators by z and .
Partially supported by the FWF grant P19147-N13. 相似文献
4.
Haïkel Skhiri 《Integral Equations and Operator Theory》2008,62(1):137-148
Let be the algebra of all bounded linear operators on a complex Banach space X and γ(T) be the reduced minimum modulus of operator . In this work, we prove that if , is a surjective linear map such that is an invertible operator, then , for every , if and only if, either there exist two bijective isometries and such that for every , or there exist two bijective isometries and such that for every . This generalizes for a Banach space the Mbekhta’s theorem [12].
相似文献
5.
Hyoung Joon Kim 《Integral Equations and Operator Theory》2008,61(1):103-120
In this paper we consider the hyperinvariant subspace problem for quasinilpotent operators. Let denote the class of quasinilpotent quasiaffinities Q in such that Q
*
Q has an infinite dimensional reducing subspace M with Q
*
Q|
M
compact. It was known that if every quasinilpotent operator in has a nontrivial hyperinvariant subspace, then every quasinilpotent operator has a nontrivial hyperinvariant subspace. Thus
it suffices to solve the hyperinvariant subspace problem for elements in . The purpose of this paper is to provide sufficient conditions for elements in to have nontrivial hyperinvariant subspaces. We also introduce the notion of “stability” of extremal vectors to give partial
solutions to the hyperinvariant subspace problem.
相似文献
6.
Let ∑ be either an oriented hyperplane or the unit sphere in
, let
be open and connected and let
be an open and connected domain in
such that
. If in
is a null solution of the Dirac operator (also called a monogenic function in
) which is continuously extendable to
, then conditions upon
are given enabling the monogenic extension of
across
. In such a way Schwarz reflection type principles for monogenic functions are established in the Spin (1) and Spin
cases. The Spin (1) case includes the classical Schwarz reflection principle for holomorphic functions in the plane. The
Spin
case deals with so-called “half boundary value problems” for the Dirac operator.
Received: 2 February 2006 相似文献
7.
Let X be a Banach space and a strongly continuous group of linear operators on X. Set and where is the unit circle and denotes the spectrum of T(t). The main result of this paper is: is uniformly continuous if and only if is non-meager. Similar characterizations in terms of the approximate point spectrum and essential spectra are also derived.
Received: 14 June 2006, Revised: 27 September 2007 相似文献
8.
Yonutz V. Stanchescu 《Combinatorica》2008,28(3):343-355
We describe the structure of three dimensional sets of lattice points, having a small doubling property. Let be a finite subset of ℤ3 such that dim = 3. If and , then lies on three parallel lines. Moreover, for every three dimensional finite set that lies on three parallel lines, if , then is contained in three arithmetic progressions with the same common difference, having together no more than terms. These best possible results confirm a recent conjecture of Freiman and cannot be sharpened by reducing the quantity
υ or by increasing the upper bounds for . 相似文献
9.
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
10.
Stephan Ramon Garcia 《Integral Equations and Operator Theory》2008,60(3):357-367
If denotes the polar decomposition of a bounded linear operator T, then the Aluthge transform of T is defined to be the operator . In this note we study the relationship between the Aluthge transform and the class of complex symmetric operators (T iscomplex symmetric if there exists a conjugate-linear, isometric involution so that T = CT*C). In this note we prove that: (1) the Aluthge transform of a complex symmetric operator is complex symmetric, (2) if T is complex symmetric, then and are unitarily equivalent, (3) if T is complex symmetric, then if and only if T is normal, (4) if and only if T
2 = 0, and (5) every operator which satisfies T
2 = 0 is necessarily complex symmetric.
This work partially supported by National Science Foundation Grant DMS 0638789. 相似文献
11.
John W. Snow 《Algebra Universalis》2008,58(1):59-71
We prove that if is a finite algebra which satisfies a nontrivial idempotent Mal’cev condition, and if Con contains a copy of an order polynomially complete lattice other than , , or Con, then Con is not hereditary.
Received March 7, 2006; accepted in final form December 5, 2006. 相似文献
12.
Let H olenote a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. An operator T ∈ L(H) is said to be strongly irreducible if T does not commute with any nontrivial idempotent. Herrero and Jiang showed that the norm-closure of the class of all strongly irreducible operators is the class of all operators with connected spectrum. This result can be considered as an approximate inverse of the Riesz decomposition theorem. In the paper, we give a more precise charact... 相似文献
13.
C. A. Stuart 《Milan Journal of Mathematics》2008,76(1):329-399
In the first part of these notes, we deal with first order Hamiltonian systems in the form where the phase space X may be infinite dimensional so as to accommodate some partial differential equations. The Hamiltonian is required to be invariant with respect to the action of a group of isometries where is skew-symmetric and JA = AJ. A standing wave is a solution having the form for some and such that . Given a solution of this type, it is natural to investigate its stability with respect to perturbations of the initial condition.
In this context, the appropriate notion of stability is orbital stability in the usual sense for a dynamical system. We present
some of the important criteria for establishing orbital stability of standing waves.
In the second part we consider the nonlinear Schr?dinger equation which provides an interesting example of this situation
where standing waves appear as time-harmonic solutions. We show how the general theory applies to this case and review what
is known about stability.
Received: January 2008 相似文献
14.
Greg Friedman 《Mathematische Annalen》2009,343(2):371-395
Cohen, Goresky, and Ji showed that there is a Künneth theorem relating the intersection homology groups to and , provided that the perversity satisfies rather strict conditions. We consider biperversities and prove that there is a Künneth theorem relating to and for all choices of and . Furthermore, we prove that the Künneth theorem still holds when the biperversity p, q is “loosened” a little, and using this we recover the Künneth theorem of Cohen–Goresky–Ji. 相似文献
15.
Pairs of numerically satisfactory solutions as for the three-term recurrence relations satisfied by the families of functions , , are given. It is proved that minimal solutions always exist, except when and z is in the positive or negative real axis, and that is minimal as whenever . The minimal solution is identified for any recurrence direction, that is, for any integer values of and . When the confluent limit , with fixed, is the main tool for identifying minimal solutions together with a connection formula; for , is the main tool to be considered. 相似文献
16.
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
17.
Linus Carlsson 《Mathematische Zeitschrift》2009,261(1):189-200
We show a sufficient condition for a domain in to be a H
∞-domain of holomorphy. Furthermore if a domain has the Gleason property at a point and the projection of the n − 1th order generalized Shilov boundary does not coincide with Ω then is schlicht. We also give two examples of pseudoconvex domains in which the spectrum is non-schlicht and satisfy several
other interesting properties.
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.
We consider one-dimensional difference Schr?dinger equations with real analytic function V(x). Suppose V(x) is a small perturbation of a trigonometric polynomial V
0(x) of degree k
0, and assume positive Lyapunov exponents and Diophantine ω. We prove that the integrated density of states is H?lder continuous for any k > 0. Moreover, we show that is absolutely continuous for a.e. ω. Our approach is via finite volume bounds. I.e., we study the eigenvalues of the problem
on a finite interval [1, N] with Dirichlet boundary conditions. Then the averaged number of these Dirichlet eigenvalues which fall into an interval
, does not exceed , k > 0. Moreover, for , this averaged number does not exceed exp , for any . For the integrated density of states of the problem this implies that for any . To investigate the distribution of the Dirichlet eigenvalues of on a finite interval [1, N] we study the distribution of the zeros of the characteristic determinants with complexified phase x, and frozen ω, E. We prove equidistribution of these zeros in some annulus and show also that no more than 2k
0 of them fall into any disk of radius exp. In addition, we obtain the lower bound (with δ > 0 arbitrary) for the separation of the eigenvalues of the Dirichlet eigenvalues over the interval [0, N]. This necessarily requires the removal of a small set of energies.
Received: February 2006, Accepted: December 2007 相似文献
20.
Let X1 and X2 be subspaces of quotients of R
OH and C
OH respectively. We use new free probability techniques to construct a completely isomorphic embedding of the Haagerup tensor
product into the predual of a sufficiently large QWEP von Neumann algebra. As an immediate application, given any 1 < q ≤ 2, our
result produces a completely isomorphic embedding of (equipped with its natural operator space structure) into with a QWEP von Neumann algebra.
Received: June 2006, Revision: June 2007, Accepted: September 2007 相似文献