共查询到20条相似文献,搜索用时 15 毫秒
1.
N. L. Vasilevski 《Integral Equations and Operator Theory》1999,34(1):107-126
Let
be the unit disk in,
be the Bergman space, consisting of all analytic functions from
, and
be the Bergman projection of
onto
. We constructC
*-algebras
, for functions of which the commutator of Toeplitz operators [T
a
,T
b
]=T
a
T
b
–T
b
T
a
is compact, and, at the same time, the semi-commutator [T
a
,T
b
)=T
a
T
b
–T
ab
is not compact.It is proved, that for each finite set =n
0,n
1, ...,n
m
, where 1=n
0
1
<...
m
, andn
k
{}, there are algebras
of the above type, such that the symbol algebras Sym
of Toeplitz operator algebras
arecommutative, while the symbol algebras Sym
of the algebras
, generated by multiplication operators
and
, haveirreducible representations exactly of dimensions n
0,n
1,..., n
m
.This work was partially supported by CONACYT Project 3114P-E9607, México. 相似文献
2.
A submanifold M
n
r
of Minkowski space
is said to be of restricted type if its shape operator with respect to the mean curvature vector is the restriction of a fixed linear transformation of
to the tangent space of M
n
r
at every point of M
n
r
. In this paper we completely classify hypersurfaces of restricted type in
. More precisely, we prove that a hypersurface of
is of restricted type if and only if it is either a minimal hypersurface, or an open part of one of the following hypersurfaces: S
k
×
, S
k
1
×
, H
k
×
, S
n
1
, H
n
, with 1kn–1, or an open part of a cylinder on a plane curve of restricted type.This work was done when the first and fourth authors were visiting Michigan State University.Aangesteld Navorser N.F.W.O., Belgium. 相似文献
3.
R. Nair 《Monatshefte für Mathematik》1998,125(3):241-253
Supposek
n denotes either (n) or (p
n) (n=1,2,...) where the polynomial maps the natural numbers to themselves andp
k denotes thek
th rationals prime. Also let
denote the sequence of convergents to a real numberx and letc
n(x))
n=1
be the corresponding sequence of partial quotients for the nearest integer continued fraction expansion. Define the sequence of approximation constants
n(x))
n=1
by
In this paper we study the behaviour of the sequences
and
for almost allx with respect to the Lebesgue measure. In the special case wherek
n=n (n=1,2,...) these results are known and due to H. Jager, G. J. Rieger and others. 相似文献
4.
Suppose that k and l are integers such that
and
, M
k is a set of numbers without kth powers, and
. In this paper, we obtain asymptotic estimates of the sums
over
相似文献
5.
For a given sequence n1 < n2 < ... of integers satisfying
and for a given convergent sequence of
complex numbers {aj}, it was shown in [4] that there is
a uniformly-almost-even function
assuming the values
f(nj) = aj.
For the proof, Gelfands theory of commutative
Banach algebras and Tietzes extension theorem were used. In [3]
an incomplete proof [by elementary means] of this result was
given.1)The aim of this note is to give some results which can be proved by the
method from [3].1)The first-named author is grateful to the second author for pointing out a missing case in the above-mentioned proof.Received: 7 November 2002 相似文献
7.
Let
be the j-fold iterated function of
. Let
and > 0 be fixed, Q be a prime, and let N
k(Q|x) denote the number of those nx for which Q
. We give the asymptotics of N
k(Q|x) in the range
. 相似文献
8.
We introduce the notion ofweak subnormality, which generalizes subnormality in the sense that for the extension
ofT
we only require that
hold forf
; in this case we call
a partially normal extension ofT. After establishing some basic results about weak subnormality (including those dealing with the notion of minimal partially normal extension), we proceed to characterize weak subnormality for weighted shifts and to prove that 2-hyponormal weighted shifts are weakly subnormal. Let {
n
}
n=0
be a weight sequence and letW
denote the associated unilateral weighted shift on
. IfW
is 2-hyponormal thenW
is weakly subnormal. Moreover, there exists a partially normal extension
on
such that (i)
is hyponormal; (ii)
; and (iii)
. In particular, if is strictly increasing then
can be obtained as
whereW
is a weighted shift whose weight sequence {
n
·
n=0
is given by
In this case,
is a minimal partially normal extension ofW
. In addition, ifW
is 3-hyponormal then
can be chosen to be weakly subnormal. This allows us to shed new light on Stampfli's geometric construction of the minimal normal extension of a subnormal weighted shift. Our methods also yield two additional results: (i) the square of a weakly subnormal operator whose minimal partially normal extension is always hyponormal, and (ii) a 2-hyponormal operator with rank-one self-commutator is necessarily subnormal. Finally, we investigate the connections of weak subnormality and 2-hyponormality with Agler's model theory.Supported by NSF research grant DMS-9800931.Supported by the Brain Korea 21 Project from the Korean Ministry of Education. 相似文献
9.
R. S. Davtyan 《Mathematical Notes》1969,6(4):725-732
It is shown that for convergence of every orthonormal system
n(x) given on [0, l],it is necessary and sufficient that, under the condition
on tlie increasing function W(x) and for
there hold
almost everywhere on [0, 1].Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 451–462, October, 1969. 相似文献
10.
Let (,G, U) be a continuous representation of a Lie groupG by bounded operatorsg U (g) on the Banach space and let (,
,dU) denote the representation of the Lie algebra
obtained by differentiation. Ifa
1, ...,a
d
is a Lie algebra basis of
,A
i
=dU (a
i
) and
whenever =(i
1, ...,i
k
) we reconsider the operators
相似文献
11.
G. A. Kalyabin 《Functional Analysis and Its Applications》2004,38(3):184-191
We solve Tikhomirov's problem on the explicit computation of sharp constants in the Kolmogorov type inequalities
12.
Nous montrons que toute fonction séparément finement surharmonique sur un ouvert de la topologie produit
n_1×s×
n_k des topologies fines des espaces R
n
1,. . ., R
n
k,
n_1×s×
n_k-localement bornée inférieurement est finement surharmonique dans . On en déduit que toute fonction séparément finement harmonique,
n_1×s×
n_k-localement bornée sur est finement harmonique dans .Separately Finely Superharmonic Functions
Abstract.We prove that every separately finely surperharmonic function on an open set in R
n
1×s×R
n
k for the product
n_1×s×
n_k of the fine topologies on the spaces R
n
1,. . ., R
n
k,
n_1×s×
n-klocally lower bounded, is finely superharmonic in . We then deduce that every separateltly finely harmonic function
n_1×s×
n
k-locally bounded in is finely harmonic. 相似文献
13.
We investigate the problem of the boundedness of the following recurrence sequence in a Banach space B:
where |y
n} and |
n
} are sequences bounded in B, and A
k, k 1, are linear bounded operators. We prove that if, for any > 0, the condition
is satisfied, then the sequence |x
n} is bounded for arbitrary bounded sequences |y
n} and |
n
} if and only if the operator
has the continuous inverse for every z C, |z| 1. 相似文献
14.
Jean-Marie De Koninck 《Monatshefte für Mathematik》1993,116(1):13-37
Let
and, for each integern such that (n)k, denote byP
k
(n) itsk
th largest prime factor. Further, given a set of primesQ of positive density <1 satisfying a certain regularity condition, defineP(n, Q), as the largest prime divisor ofn belonging toQ, assuming thatP(n,Q)=+ if no such prime factor exists. We provide estimates of
, fork2, and of
. We also study the median value of the functionP(n,Q) and that of the functionP
k
(n) for eachk1. 相似文献
15.
In the view-obstruction problem, congruent, closed convex bodies centred at the points
in
n
are expanded uniformly until they block all rays from the origin into the open positive cone. The central problem is to determine the minimal blocking size. In the case of spheres of diameter 1 and cubes of side 1 these values are known forn=2, 3 and 4. Here we show that in 5, this value for the sphere of diameter 1 is
. 相似文献
16.
On the ascending star subgraph decomposition of star forests 总被引:3,自引:0,他引:3
LetG be a graph of size
for some integern2. ThenG is said to have an ascending star subgraph decomposition ifG can be decomposed inton subgraphsG
1,G
2, ...,G
n such that eachG
i is a star of sizei with 1in. We shall prove in this paper that a star forest with size
, possesses an ascending star subgraph decomposition if the size of each component is at leastn, which is stronger than the conjecture proposed by Y. Alavi, A. J. Boals, G. Chartrand, P. Erds and O. R. Oellermann. 相似文献
17.
O. M. Fomenko 《Journal of Mathematical Sciences》2004,122(6):3699-3708
Let S
k
(0(N)) be the space of cusp forms of even weight k for
0
(N), let
be the set of all newforms in S
k
(
0
(N)), and let
be the symmetric square of the Hecke L-function of a form
. It is proved that for N=p we have
18.
One investigates the scattering theory for the positive self-adjoint operatorH=–· acting in
with = × and a bounded open set in
n–1,n2. The real-valued function belongs toL
(), is bounded from below byc>0 and there exist real-valued functions
1 and
2 inL
() such that –
j
,j=1,2 is a short range perturbation of
j
when (–1)
j
x
n
+. One assumes
j
=
(j)
1R,j=1,2, with
(j)
L
bounded from below byc>0. One proves the existence and completeness of the generalized wave operators
j
±
=s –
j
e
–itHj
,j=1,2, withH
j
=–·
j
and
j
: equal to 1 if (–1)
j
x
n
>0 and to 0 if (–1)
j
x
n
<0. The ranges ofW
j
±
:=(
j
±
)* are characterized so that
W
1
±
=Ran and
. The scattering operator can then be defined. 相似文献
19.
Raúl Figueroa 《Geometriae Dedicata》1994,50(2):205-216
Let be a non-Desarguesian semifield plane of orderp
n, p a prime number 5 andn3, and let
denote the group induced by the autotopism groupG of on the line at infinity. We prove that is a generalized twisted field plane if, and only if,
has an element of order (p
k–1)((p
n–1)/(p
m–1)), for some integersk andm, wherek | m, m | n, andm
20.
A. Schinzel 《Monatshefte für Mathematik》1986,102(4):309-337
Letk>1 and let
be non-zero algebraic numbers contained in the field
. It is shown that for almost all, in the sense of density integer vectorsn
1,...,n
k
the polynomial
becomes irreducible over
on dividing by the product of all factorsx–, where is a root of unity.Dedicated to Professor E. Hlawka on the occasion of his seventieth birthday 相似文献
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