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1.
Let Q be a regular operator valued generalized Nevanlinna function with negative index , i.e.
. It is shown that then there exists a rational function B(z), which collects the generalized poles and zeros of Q that are not of positive type such that the function belongs to the Nevanlinna class
.The author acknowledges support of the Fonds zur Förderung der wissenschaftlichen Forschung of Austria, Project P 12176 MAT, and of the EU Research Training Network, Contract No. HPRN-CT-2000-00116. 相似文献
2.
Given a nonempty set
and two multifunctions
, we consider the following generalized quasi-variational inequality problem associated with X, : Find
such that
. We prove several existence results in which the multifunction is not supposed to have any continuity property. Among others, we extend the results obtained in Ref. 1 for the case ( x( X. 相似文献
3.
We give here a rigorous formulation for a pair of consecutive simple positive zeros of the function H
0 (which is closely related to the Riemann -function) to be a Lehmer pair of zeros of H
0. With this formulation, we establish that each such pair of zeros gives a lower bound for the de Bruijn-Newman constant (where the Riemann Hypothesis is equivalent to the assertion that 0). We also numerically obtain the following new lower bound for : |
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4.
In this paper we extend necessary conditions for Fredholmness of singular integral operators with piecewise continuous coefficients in rearrangement-invariant spaces [19] to the weighted case X(, w). These conditions are formulated in terms of indices ( Q
t
w) and ( Q
t
w) of a submultiplicative function Q
t
w, which is associated with local properties of the space, of the curve, and of the weight at the point t. Using these results we obtain a lower estimate for the essential norm | S| of the Cauchy singular integral operator S in reflexive weighted rearrangement-invariant spaces X(, w) over arbitrary Carleson curves : where
. In some cases we give formulas for computation of ( Q
t
w) and ( Q
t
w). 相似文献
5.
Given
and a sequence of Dirichlet polynomials
estimates for the coefficients a
n are proved if { n} is uniformly bounded on a region containing a half plane. Thereby a result is obtained which is an analogue of a known result for polynomials, that is for the A-transforms of the geometric sequence; moreover a Jentzsch type theorem for { n( z)} is derived. 相似文献
6.
Let
be a semilinear hyperbolic system, where A is a real diagonal matrix and a mapping yF(x, t, y) is in
with uniform bounds for ( x, t) K 2. Oberguggenberger [6] has constructed a generalized solution to (1) when A is an arbitrary generalized function and F has a bounded gradient with respect to y for ( x, t) K 2. The above system, in the case when the gradient of the nonlinear term F with respect to y is not bounded, is the subject of this paper. F is substituted by F
h() which has a bounded gradient with respect to y for every fixed (, ) and converges pointwise to F as 0. A generalized solution to is obtained. It is compared to a continuous solution to (1) (if it exists) and the coherence between them is proved. 相似文献
7.
Continuing previous work, we discuss applications of our summation/integration procedure to some classes of complex slowly convergent series. Especially, we consider the series of the form
, where 0< v1 and R(s) is a rational function. Such cases were recently studied by Gautschi, using the Laplace transform method. Also, we give an appropriate method for calculating values of the Riemann zeta function
, which can be transformed to a weighted integral on (0,+)of the function t exp (– z/2)log(1-
m
2
t
2))cos( z arctan(
m
t,
m
>=2/((2 m+1)), m0, involving the hyperbolic weight w(t)=1/cosh 2
t. Numerical results are included to illustrate the method.Dedicated to Luigi Gatteschi on the occasion of his 70th birthday 相似文献
8.
In this paper we study the spaces of continuous functions f on 2 satisfying |
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9.
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.
The function , is a characteristic function of a probability distribution iff
. This distribution is absolutely continuous; for =0 it is symmetric. The latter case was introduced by Linnik in 1953 [13] and several applications were found later. The case 0 was introduced by Klebanov, Maniya, and Melamed in 1984 [9], while some special cases were considered previously by Laha [12] and Pillai [18]. In 1994, Kotz, Ostrovskii and Hayfavi [10] carried out a detailed investigation of analytic and asymptotic properties of the density of the distribution for the symmetric case =0. We generalize their results to the non-symmetric case 0. As in the symmetric case, the arithmetical nature of the parameter plays an important role, but several new phenomena appear. 相似文献
11.
For a given function b in the unit ball of H
and an arbitrary H
function m, the question of when m is a multiplier of the de Branges space
(that is, when
is invariant under multiplication by m) is examined. Some necessary and sufficient conditions that m be a multiplier of
are found and it is shown that there are no nonconstant inner multipliers of
when b is a nonconstant extreme point of the unit ball of H
. A new proof is given of the known fact that
is invariant under multiplication by z when b is not an extreme point of the unit ball of H
. Finally, we give a new proof of the known fact that an inner function m is a multiplier of
for b(z)=(1+ z)/2 if and only if m belongs to the range of
.Some of the work in this paper originally appeared in the author's doctoral disseratation written at the University of California at Berkeley under the supervision of Donald Sarason. 相似文献
12.
In the present paper we obtain a sufficient condition for the exponential dichotomy of a strongly continuous, one-parameter
semigroup , in terms of the admissibility of the pair . It is already known the equivalence between the -admissibility condition and and the hyperbolicity of a C
0-semigroup , when we assume a priori that the kernel of the dichotomic projector (denoted here by X
2) is T( t)-invariant and is an invertible operator. We succeed to prove in this paper that the admissibility of the pair still implies the existence of an exponential dichotomy for a C
0-semigroup even in the general case where the kernel of the dichotomic projector, X
2, is not assumed to be T( t)-invariant.
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13.
Let K
p(u 1, ..., u p) be the complete p-partite graph whose ith vertex class has u
i vertices (l ip). We show that the theorem of Erds and Stone can be extended as follows. There is an absolute constant >0 such that, for all r1, 0<1 and=">1/ r, every graph G=G
n of sufficiently large order | G|= n with at least |
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14.
There is an algebra of commutative differential-difference operators which is very useful in studying analytic structures invariant under permutation of coordinates. This algebra is generated by the Dunkl operators
, ( i=1, ..., N, where ( ij) denotes the transposition of the variables x
i
x
j
and k is a fixed parameter). We introduce a family of functions { p
}, indexed by m-tuples of non-negative integers = ( 1, ...,
m
) for mN, which allow a workable treatment of important constructions such as the intertwining operator V. This is a linear map on polynomials, preserving the degree of homogeneity, for which
, i = 1, ..., N, normalized by V1=1 (see Dunkl, Canadian J. Math. 43 (1991), 1213–1227). We show that T
i
p
=0 for i>m, and where ( 1, 2, ...,
m
) is the partition whose parts are the entries of (That is, 1 2 ...
m
0), = ( 1, ...,
m
),
i=1
m
i
=
i=1
m
m
and the sorting of is a partition strictly larger than in the dominance order. This triangular matrix representation of V allows a detailed study. There is an inner product structure on span { p
} and a convenient set of self-adjoint operators, namely T
ii
, where ip p( 1, ....,
i
+ 1, ...,
m
). This structure has a bi-orthogonal relationship with the Jack polynomials in m variables. Values of k for which V fails to exist are called singular values and were studied by De Jeu, Opdam, and Dunkl in Trans. Amer. Math. Soc. 346 (1994), 237–256. As a partial verification of a conjecture made in that paper, we construct, for any a=1,2,3,... such that gcd( N–m+1, a)<( N–m+1)/ m and mN/2, a space of polynomials annihilated by each T
i
for k=–a/(N–m+1) and on which the symmetric group S
N
acts according to the representation ( N–m, m).During the research for this paper, the author was partially supported by NSF grant DMS-9401429, and also held a Sesquicentennial Research Associateship at the University of Virginia 相似文献
15.
A 2-periodic continuous real function f is said to be periodically monotone if it has the following property: there exist number t
1t
2t
3t
1+2 such that f is nonincreasing for t
1t
2 and nondecreasing in t
2tt
3. For any 2-periodic, integrable real function g with
0
2
| g( t| dt) we define |
相似文献
16.
Let
be a C*-algebra and X a Hilbert C*
-module. If
is a projection, let
be the p-sphere of X. For φ a state of
with support p in
and
consider the modular vector state φ x of
given by
The spheres
provide fibrations
and
These fibrations enable us to examine the homotopy type of the sets of modular vector states, and relate it to the homotopy type of unitary groups and spaces of projections. We regard modular vector states as generalizations of pure states to the context of Hilbert C*-modules, and the above fibrations as generalizations of the projective fibration of a Hilbert space. 相似文献
18.
In this paper we consider the magnetic Couette-Taylor problem, that is, a conducting fluid between two infinite rotating cylinders, subject to a magnetic field parallel to the rotation axis. This configuration admits an equilibrium solution of the form
It is shown that this equilibrium is Ljapounov stable under small perturbations in
where
provided that the parameters a, b, , are small. The methods of proof are a combination of an energy method, based on Bloch space analysis and small data techniques.Received: February 5, 2003; revised: September 29, 2003Dedicated to Prof. H. Amann on the occasion of his 65. birthday 相似文献
19.
In many problems the local zero-pole structure (i.e. locations of zeros and poles together with their orders) of a scalar rational function w is a key piece of structure. Knowledge of the order of the pole or zero of the rational function w at the point is equivalent to knowledge of the
-module
(where
is the space of rational functions analytic at ). For the more intricate case of a rational p×m matrix function W, we consider the structure of the module
as the appropriate analogue of zero-pole structure (location of zeros and poles together with directional information), where
is the set of column vectors of height m with entries equal to rational functions which are analytic at . Modules of the form
in turn can be explicitly parametrized in terms of a collection of matrices ( C
, A
, B
, B
,
) together with a certain row-reduced (p–m)×m matrix polynomial P(z) (which is independent of ) which satisfy certain normalization and consistency conditions. We therefore define the collection ( C
, A
, Z
, B
,
, P(z)) to be the local spectral data set of the rational matrix function W at . We discuss the direct problem of how to compute the local spectral data explicitly from a realization W(z)=D+C(z–A)
–1
B for W and solve the inverse problem of classifying which collections ( C
, A
, Z
, B
,
, P(z)) satisfying the local consistency and normalization conditions arise as the local spectral data sets of some rational matrix function W. Earlier work in the literature handles the case where W is square with nonzero determinant. 相似文献
20.
Let n be a positive integer and let X be a linear space over a commutative field K. In the set = (K\{0}) × X we define a binary operation ·: × by
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