共查询到20条相似文献,搜索用时 46 毫秒
1.
The asymptotic estimate for the expected number of real zeros of a random algebraic polynomial
is known. The identical random coefficients aj(ω) are normally distributed defined on a probability space
, ω ∈Ω. The estimate for the expected number of zeros of the derivative of the above polynomial with respect to x is also known, which gives the expected number of maxima and minima of Qn(x, ω). In this paper we provide the asymptotic value for the expected number of zeros of the integration of Qn(x,ω) with respect to x. We give the geometric interpretation of our results and discuss the difficulties which arise when we consider a similar
problem for the case of
. 相似文献
2.
Egor A. Alekhno 《Positivity》2009,13(1):3-20
Let T be a positive operator on a Banach lattice E. Some properties of Weyl essential spectrum σew(T), in particular, the equality , where is the set of all compact operators on E, are established. If r(T) does not belong to Fredholm essential spectrum σef(T), then for every a ≠ 0, where T−1 is a residue of the resolvent R(., T) at r(T). The new conditions for which implies , are derived. The question when the relation holds, where is Lozanovsky’s essential spectrum, will be considered. Lozanovsky’s order essential spectrum is introduced. A number of
auxiliary results are proved. Among them the following generalization of Nikol’sky’s theorem: if T is an operator of index zero, then T = R + K, where R is invertible, K ≥ 0 is of finite rank. Under the natural assumptions (one of them is ) a theorem about the Frobenius normal form is proved: there exist T-invariant bands such that if
, where , then an operator on Di is band irreducible.
相似文献
3.
We study the application,
, where
is the
supremum of positive s such that the problem
admits a solution. Where B 1 is the unit ball in
We show that
is a decreasing function, with
where
is the unique solution of the
problem
.
We also give the explicit solutions of the problem
, when
and show that
. We show that the problem
doesnt admit a solution.
In the end, we give a numerical approximation of
, when
. 相似文献
4.
We show that if A is a separable, nuclear,
-absorbing (or strongly purely infinite) C*-algebra which is homotopic to zero in an ideal-system preserving way, then A is the inductive limit of C*-algebras of the form
where Γ is a finite connected graph (and
is the algebra of continuous functions on Γ that vanish at a distinguished point
).We show further that if B is any separable, nuclear C*-algebra, then
is isomorphic to a crossed product
where D is an inductive limit of C*-algebras of the form
(and D is
-absorbing and homotopic to zero in an ideal-system preserving way).Received: December 2003 Revision: July 2004 Accepted: July 2004 相似文献
5.
Onur Yavuz 《Integral Equations and Operator Theory》2007,58(3):433-446
We consider a multiply connected domain
where
denotes the unit disk and
denotes the closed disk centered at
with radius r
j
for j = 1, . . . , n. We show that if T is a bounded linear operator on a Banach space X whose spectrum contains ∂Ω and does not contain the points λ1, λ2, . . . , λ
n
, and the operators T and r
j
(T − λ
j
I)−1 are polynomially bounded, then there exists a nontrivial common invariant subspace for T
* and (T − λ
j
I)*-1. 相似文献
6.
A theorem of Sz.-Nagy and Foias [9] shows that the characteristic function
of a completely non-unitary contraction T is a complete unitary invariant for T. In this note we extend this theorem to the case of a pure commuting contractive tuple using a natural generalization of the characteristic function to an operator-valued analytic function defined on the open unit ball of
This function is related to the curvature invariant introduced by Arveson [3]. 相似文献
7.
For a contraction operator T with spectral radius less than one on a Banach space
, it is shown that the factorization of certain L1 functions by vectors x in
and x*. in
, in the sense that
for n ≧ 0, implies the existence of invariant subspaces for T. Explicit formulae for such factorizations are given in the case of weighted composition operators on reproducing kernel
Hilbert spaces. An interpolation result of McPhail is applied to show how this can be used to construct invariant subspaces
of hyperbolic weighted composition operators on H2.
Received: 1 November 2005 相似文献
8.
Carlos E. Durán Luis E. Mata-Lorenzo Lázaro Recht 《Integral Equations and Operator Theory》2005,53(1):33-50
This article focuses on the study of the metric geometry of homogeneous spaces
(the unitary group of a C*-algebra
modulo the unitary group of a C*-subalgebra
) where the invariant Finsler metric in
is induced by the quotient norm of
Under the assumption that
is of compact type, i.e. when the unitary group is relatively compact in the strong operator topology, this work presents local and global versions of Hopf-Rinow-like theorems: given points
there exists a minimal uniparametric group curve joining ρ0 and ρ1. 相似文献
9.
M. A. Bastos C. A. Fernandes Yu. I. Karlovich 《Integral Equations and Operator Theory》2006,55(1):19-67
We establish a symbol calculus for the C*-subalgebra
of
generated by the operators of multiplication by slowly oscillating and piecewise continuous functions and the operators
where
is the Cauchy singular integral operator and
The C*-algebra
is invariant under the transformations
where Uz is the rotation operator
Using the localtrajectory method, which is a natural generalization of the Allan-Douglas local principle to nonlocal type
operators, we construct symbol calculi and establish Fredholm criteria for the C*-algebra
generated by the operators
and
for the C*-algebra
generated by the operators
and
and for the C*-algebra
generated by the algebras
and
The C*-algebra
can be considered as an algebra of convolution type operators with piecewise slowly oscillating coefficients and shifts acting
freely. 相似文献
10.
Violeta Petkova 《Archiv der Mathematik》2005,84(4):311-324
Let
be a weighted space with weight . In this paper we show that for every Wiener-Hopf operator T on
and for every a I, there exists a function
such that
for all
Here (g)a denotes the function x g(x)eax for
and
where R+ is the spectral radius of the shift S : f(x) f(x–1) on
while
is the spectral radius of the backward shift S–1 : f(x) (P+f)(x+1) on
Moreover, there exists a constant C, depending on , such that
for every a I. If R– < R+, we prove that there exists a bounded holomorphic function v on
such that for
the function va is the restriction of v on the line
Received: 18 May 2004 相似文献
11.
The C*-algebra
generated by the Bergman and anti-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space L2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky results on two-dimensional singular integral operators with coefficients admitting homogeneous discontinuities we reduce the study to simpler C*-algebras associated with points
and pairs
We construct a symbol calculus for unital C*-algebras generated by n orthogonal projections sum of which equals the unit and by m one-dimensional orthogonal projections. Such algebras are models of local algebras at points z ∈∂Π being the discontinuity points of coefficients. A symbol calculus for the C*- algebra
and a Fredholm criterion for the operators
are obtained. Finally, a C*-algebra isomorphism between the quotient algebra
where
is the ideal of compact operators, and its analogue
for the unit disk is constructed. 相似文献
12.
In this paper we construct certain moduli spaces, which we call
moduli spaces of (principal) F-bundles,
and study their basic properties. These spaces are
associated to triples consisting of a smooth projective geometrically
connected curve over a finite field, a split
reductive group G, and an irreducible
algebraic representation
.of
of
Our spaces generalize moduli
spaces of F-sheaves, studied
by Drinfeld and Lafforgue, which correspond to the case G
= GLr
and
is the tensor product of the standard
representation and its dual. The importance of the moduli spaces
of F-bundles is due to the
belief that Langlands correspondence is realized in their cohomology. 相似文献
13.
In this paper we solve moment problems for Poisson transforms and, more generally, for completely positive linear maps on unital C*-algebras generated by universal row contractions associated with
, the free semigroup with n generators. This class of C*-algebras includes the Cuntz-Toeplitz algebra
(resp.
) generated by the creation operators on the full (resp. symmetric, or anti-symmetric)) Fock space with n generators. As consequences, we obtain characterizations for the orbits of contractive Hilbert modules over complex free semigroup algebras such as
,and, more generally, the quotient algebra
, where J is an arbitrary two-sided ideal of
. All these results are extended to the generalized Cuntz algebra
, where Gi+ are the positive cones ofdiscrete subgroups Gi+ of the real line
. Moreover, we characterize the orbits of Hilbert modules over the quotient algebra
, where J is an arbitrary two-sided ideal ofthe free semigroup algebra
. 相似文献
14.
Structure of Degenerate Block Algebras 总被引:13,自引:0,他引:13
Given a non-trivial torsion-free abelian group (A,+,Q), a field F of characteristic 0, and a non-degenerate bi-additive skew-symmetric map
: A
A
F, we define a Lie algebra
=
(A,
) over F with basis {ex | x
A/{0}} and Lie product [ex,ey] =
(x,y)ex+y. We show that
is endowed uniquely with a non-degenerate symmetric invariant bilinear form and the derivation algebra Der
of
is a complete Lie algebra. We describe the double extension D(
, T) of
by T, where T is spanned by the locally finite derivations of
, and determine the second cohomology group H2(D(
, T),F) using anti-derivations related to the form on D(
, T). Finally, we compute the second Leibniz cohomology groups HL2(
, F) and HL2(D(
, T), F).2000 Mathematics Subject Classification: 17B05, 17B30This work was supported by the NNSF of China (19971044), the Doctoral Programme Foundation of Institution of Higher Education (97005511), and the Foundation of Jiangsu Educational Committee. 相似文献
15.
The C
*-algebra
generated by the n poly-Bergman and m antipoly-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space
L
2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky
results on two-dimensional convolution operators with symbols admitting homogeneous discontinuities we reduce the study to
simpler C
*-algebras associated with points
and pairs
. Applying a symbol calculus for the abstract unital C
*-algebras generated by N orthogonal projections sum of which equals the unit and by M = n + m one-dimensional orthogonal projections and using relations for the Gauss hypergeometric function, we study local algebras
at points
being the discontinuity points of coefficients. A symbol calculus for the C
*-algebra
is constructed and a Fredholm criterion for the operators
is obtained. 相似文献
16.
In the present paper we suggest an explicit construction of a Cartan connection for an elliptic or hyperbolic CR manifold
M of dimension six and codimension two, i.e. a pair
, consisting of a principal bundle
over M and of a Cartan connection form
over P, satisfying the following property: the (local) CR transformations
are in one to one correspondence with the (local) automorphisms
for which
. For any
, this construction determines an explicit monomorphism of the stability subalgebra Lie (Aut(M)x) into the Lie algebra
of the structure group H of P.
Mathematics Subject Classification (2000) Primary 32V05, Secondary 53C15, 53A55 相似文献
17.
Pascale Vitse 《Archiv der Mathematik》2005,85(4):374-385
For Banach space operators T satisfying the Tadmor-Ritt condition
a band limited H∞ calculus is established,
where
and a is at most of the order C(T)5. It follows that such a T allows a bounded Besov algebra B∞ 10 functional calculus,
These estimates are sharp in a convenient sense. Relevant embedding theorems for B∞ 10 are derived.
Received: 25 October 2004; revised: 31 January 2005 相似文献
18.
On the Range of the Aluthge Transform 总被引:1,自引:0,他引:1
Let
be the algebra of all bounded linear operators on a complex separable Hilbert space
For an operator
let
be the Aluthge transform of T and we define
for all
where T = U|T| is a polar decomposition of T. In this short note, we consider an elementary property of the range
of Δ. We prove that R(Δ) is neither closed nor dense in
However R(Δ) is strongly dense if
is infinite dimensional.
An erratum to this article is available at . 相似文献
19.
If
is an initially hereditary family of finite subsets of positive integers (i.e., if
and G is initial segment of F then
) and M an infinite subset of positive integers then we define an ordinal index
. We prove that if
is a family of finite subsets of positive integers such that for every
the characteristic function χF is isolated point of the subspace
of { 0,1 }N with the product topology then
for every
infinite, where
is the set of all initial segments of the members of
and ω1 is the first uncountable ordinal. As a consequence of this result we prove that
is Ramsey, i.e., if
is a partition of
then there exists an infinite subset M of positive integers such that
where [M]< ω is the family of all finite subsets of M. 相似文献
20.
We introduce a notion of energy for harmonic currents of bidegree (1, 1) on a complex K?hler manifold (M, ω). This allows us to define
for positive harmonic currents. We then show that for a lamination with singularities of a compact set in
without directed positive closed currents, there is a unique positive harmonic current which minimizes energy. If X is a compact laminated set in
of class
it carries a unique positive harmonic current T of mass 1. The current T can be obtained by an Ahlfors type construction starting with an arbitrary leaf of X. When X has a totally disconnected set of singularities, contained in a countable union of analytic sets, the above construction
still gives positive harmonic currents.
Received: February 2004 Revision: December 2004 Accepted: June 2005 相似文献