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1.
Let Cp be the Schatten p-class for p>0. Generalizations of the parallelogram law for the Schatten 2-norms have been given in the following form: if A={A1,A2,…,An} and B={B1,B2,…,Bn} are two sets of operators in, then C2
2.
The paper is concerned with the fine properties of monotone functions on . We study the continuity and differentiability properties of these functions, the approximability properties, the structure of the distributional derivatives and of the weak Jacobians. Moreover, we exhibit an example of a monotone function u which is the gradient of a convex function and whose weak Jacobian Ju is supported on a purely unrectifiable set. Received October 9, 1996; in final form April 21, 1997 相似文献
3.
4.
Milutin R. Dostanić 《Mathematische Zeitschrift》2001,236(3):453-459
We prove that for every Volterra operator T the inequality holds, where b is an absolute constant and are its singular values. Received January 26, 2000 / Published online February 5, 2001 相似文献
5.
6.
7.
Summary.
This paper presents general algorithms for the parallel
solution of
finite element problems associated with maximal monotone operators of local
type. The latter concept, which is also introduced here, is well suited to
capture the idea that the given operator is the discretization of a differential
operator that may involve nonlinearities and/or constraints as long as those are
of a local nature. Our algorithms are obtained as a combination of known
algorithms for possibly multi-valued maximal monotone operators with appropriate
decompositions of the domain. This work extends a method due to two of the
authors in the single-valued and linear case.
Received April 25, 1994 相似文献
8.
We give a matrix version of the scalar inequality f(a + b) ? f(a) + f(b) for positive concave functions f on [0, ∞). We show that Choi’s inequality for positive unital maps and operator convex functions remains valid for monotone convex functions at the cost of unitary congruences. Some inequalities for log-convex functions are presented and a new arithmetic-geometric mean inequality for positive matrices is given. We also point out a simple proof of the Bhatia-Kittaneh arithmetic-geometric mean inequality. 相似文献
9.
We try to find a continuous functionu defined on a real right half-line with the range (0, ) such thatu
–1 is operator monotone. We then look for another functionv such thatv(u
–1) is operator monotone, namely,u(A)u(B) impliesv(A)v(B) for self-adjoint operatorsA andB. 相似文献
10.
Numerical verification of solutions for variational inequalities 总被引:1,自引:0,他引:1
In this paper, we consider a numerical technique that enables us to verify the existence of solutions for variational inequalities.
This technique is based on the infinite dimensional fixed point theorems and explicit error estimates for finite element approximations.
Using the finite element approximations and explicit a priori error estimates for obstacle problems, we present an effective
verification procedure that through numerical computation generates a set which includes the exact solution. Further, a numerical
example for an obstacle problem is presented.
Received October 28,1996 / Revised version received December 29,1997 相似文献
11.
Gilles Pisier 《Mathematische Zeitschrift》2000,235(1):53-81
For every integer , there is a unital closed subalgebra with similarity degree equal precisely to d, in the sense of our previous paper. This means that for any unital homomorphism we have with independent of u, and the exponent d in this estimate cannot be improved. The proof that the degree is larger than crucially uses an upper bound for the norms of certain Gaussian random matrices due to Haagerup and Thorbj?rnsen. We also
include several complements to our previous publications on the same subject.
Received: 25 April, 1999; Accepted: 23 June, 1999 相似文献
12.
Julien Vovelle 《Numerische Mathematik》2002,90(3):563-596
Summary. This paper is devoted to the study of the finite volume methods used in the discretization of conservation laws defined on
bounded domains. General assumptions are made on the data: the initial condition and the boundary condition are supposed to
be measurable bounded functions. Using a generalized notion of solution to the continuous problem (namely the notion of entropy
process solution, see [9]) and a uniqueness result on this solution, we prove that the numerical solution converges to the
entropy weak solution of the continuous problem in for every . This also yields a new proof of the existence of an entropy weak solution.
Received May 18, 2000 / Revised version received November 21, 2000 / Published online June 7, 2001 相似文献
13.
Summary.
With denoting the -th partial
sum of ${\rm e}^{z}$, the exact rate of convergence of the zeros of the
normalized partial sums, , to the Szeg\"o curve
was
recently studied by Carpenter et al. (1991), where
is defined by
Here, the above results are generalized to the convergence of
the zeros and poles of certain sequences of normalized Pad\'{e}
approximants
to , where is the associated Pad\'{e} rational approximation to .
Received February 2, 1994 相似文献
14.
Alexander Ženíšek 《Numerische Mathematik》1995,71(3):399-417
Summary.
The finite element method for an elliptic equation with discontinuous
coefficients (obtained for the magnetic potential from Maxwell's
equations) is analyzed in the union of closed domains the boundaries
of which form a system of three circles with the same centre.
As the middle domain is very narrow the triangulations obeying
the maximum angle condition are considered. In the case of piecewise
linear trial functions the maximum rate of
convergence in the norm
of the space is proved
under the following conditions:
1. the exact solution
is piecewise of class ;
2. the family of subtriangulations
of the narrow
subdomain satisfies the maximum angle condition
expressed by relation (38). The paper extends the results of [24].
Received
March 8, 1993 / Revised version received November 28, 1994 相似文献
15.
Let
So is the collection of all n + 1 term exponential sums with constant first term. We prove the following two theorems.
Theorem 1 (Remez-type inequality for
$E_n$
at 0).
Let
$s \in \left( 0, \frac 12 \right]\,.$
There are absolute constants
$c_1 > 0$
and
$c_2 > 0$
such that
where the supremum is taken for all
$f \in E_n$
satisfying
Theorem 2 (Nikolskii-type inequality for
$E_n$
).
There are absolute constants
$c_1 > 0$
and
$c_2 > 0$
such that
for every
$a < y < b$
and
$q > 0\,.$
It is quite remarkable that, in the above Remez- and Nikolskii-type inequalities, behaves like , where denotes the collection of all algebraic polynomials of degree at most n with real coefficients.
Received: 4 November 1998 / in final form: 2 March 1999 相似文献
16.
Jean Bertoin 《Probability Theory and Related Fields》1999,114(1):97-121
We investigate the nature of the intersection of two independent regenerative sets. The approach combines Bochners subordination
and potential theory for a pair of Markov processes in duality.
Received: 21 November 1997 / Revised version: 31 August 1998 相似文献
17.
Summary.
For univariate functions the Kronecker theorem, stating the equivalence
between the existence of an infinite block in the table of Padé approximants
and the approximated function being rational, is well-known.
In [Lubi88] Lubinsky proved that if is not rational, then its Padé table
is normal almost everywhere: for an at most countable set of points the
Taylor series expansion of is such that it generates a non-normal
Padé table. This implies that the Padé operator is an almost always
continuous operator because it is continuous when computing a normal
Padé approximant [Wuyt81].
In this paper we generalize the above results to the case of multivariate
Padé approximation. We distinguish between two different approaches for
the definition of multivariate Padé approximants: the general order one
introduced in [Levi76, CuVe84] and the so-called homogeneous one discussed
in [Cuyt84].
Received December 19, 1994 相似文献
18.
M. I. Gil' 《manuscripta mathematica》1999,100(2):213-219
Residual bounds for perturbed simple eigenvectors of linear operators are derived. Received: 27 January 1999 相似文献
19.
Approximation by translates of refinable functions 总被引:23,自引:0,他引:23
Summary.
The functions
are
refinable if they are
combinations of the rescaled and translated functions
.
This is very common in scientific computing on a regular mesh.
The space of approximating functions with meshwidth
is a
subspace of with meshwidth
.
These refinable spaces have refinable basis functions.
The accuracy of the computations
depends on , the
order of approximation, which is determined by the degree of
polynomials
that lie in .
Most refinable functions (such as scaling functions in the theory
of wavelets) have no simple formulas.
The functions
are known only through the coefficients
in the refinement equation – scalars in the traditional case,
matrices for multiwavelets.
The scalar "sum rules" that determine
are well known.
We find the conditions on the matrices
that
yield approximation of order
from .
These are equivalent to the Strang–Fix conditions on the Fourier
transforms
, but for refinable
functions they can be explicitly verified from
the .
Received
August 31, 1994 / Revised version received May 2, 1995 相似文献
20.
Heike Faßbender 《Numerische Mathematik》1997,77(3):323-345
Summary. This paper explores the relationship between certain inverse unitary eigenvalue problems and orthogonal functions. In particular,
the inverse eigenvalue problems for unitary Hessenberg matrices and for Schur parameter pencils are considered. The Szeg?
recursion is known to be identical to the Arnoldi process and can be seen as an algorithm for solving an inverse unitary Hessenberg
eigenvalue problem. Reformulation of this inverse unitary Hessenberg eigenvalue problem yields an inverse eigenvalue problem
for Schur parameter pencils. It is shown that solving this inverse eigenvalue problem is equivalent to computing Laurent polynomials
orthogonal on the unit circle. Efficient and reliable algorithms for solving the inverse unitary eigenvalue problems are given
which require only O() arithmetic operations as compared with O() operations needed for algorithms that ignore the structure of the problem.
Received April 3, 1995 / Revised version received August 29, 1996 相似文献