共查询到20条相似文献,搜索用时 13 毫秒
1.
2.
Summary In this paper, we derive a fast algorithm for the scalar Nevanlinna-Pick interpolation. Givenn distinct pointsz
i
in the unit disk |z|<1 andn complex numbersw
i
satisfying the Pick condition for 1in, the new Nevanlinna-Pick interpolation algorithm requires onlyO(n) arithmetic operations to evaluate the interpolatory rational function at a particular value ofz, in contrast to the classical algorithm which requiresO(n
2) arithmetic operations to compute the so-called Fenyves array (which is inherent in the classical algorithm). The new algorithm bypasses the generation of the Fenyves array to speed up the computation, and also yields a parallel scheme requiring onlyO(logn) arithmetic operations on a concurrent-read, exclusive-write parallel random access machine withn processors. We must remark that the rational functionf(z) computed by the new algorithm is one degree higher than the function computed by the classical algorithm.Supported in part by the US Army Research Office Grant No. DAAL03-91-G-0106 相似文献
3.
We study theC
*-algebras generated by projective isometric representations of semigroups, using a dilation theorem and the stucture theory of twisted crossed products. These algebras include the Toeplitz algebras of noncommutative tori recently studied by Ji, and similar algebras associated to the twisted group algebras of other groups such as the integer Heisenberg group. 相似文献
4.
Andrew T. Tomerlin 《Integral Equations and Operator Theory》2000,37(3):350-356
An example is given which clarifies the present situation of the operator norm convergence of Trotter-Kato product formula. It shows that the rate of convergence of the formula with respect to the operator norm obtained in [NZ2] is best possible. It also yields a counter-example of the operator norm convergence of the formula in another case. 相似文献
5.
6.
Nevanlinna-Pick interpolation with boundary data 总被引:4,自引:0,他引:4
Donald Sarason 《Integral Equations and Operator Theory》1998,30(2):231-250
Versions of the Nevanlinna-Pick interpolation problem with boundary interpolation nodes and boundary interpolated values are investigated. 相似文献
7.
It is known [KRS] that for each finitely generated Banach algebra
there exists a numberN such that for eachn>N the matrix algebras
can be generated by three idempotents. In this paper we show that the same statement is true for direct sums
and
, where
is a finitely generated free algebra, i.e. polynomials in several non-commuting variables. These results are new even for
algebras
because the numberN we obtain here improves known estimates (see for example [R]). We show that the algebra
can be generated by two idempotents if and only ifn
j
=2 for eachj and
is singly generated. Also we give an example of a free singly generated algebra
for which
can not be generated by two idempotents. But% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn%
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x%
fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacuWFSeIqgaacaaaa!409A!\[{\tilde
{\cal B}}\] can be generated by three idempotents for each singly generated free algebra
. 相似文献
8.
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
9.
LetA be aC
* — algebra for which all irrèducible representations are of dimensional n. Then ([F], [TT], [V]) algebraA is isomorphic to algebra of all continuous sections of an appropriate algebraic bundle
A
. The basisX of this bundle coincides with the compact of all maximal two-sided ideals ofA. We obtain some conditions which provide that
A
is trivial and this yields thatA is isomorphic to the algebra of alln×n matrix functions continuous onX. In the case whenX=S
n
is a sphere we describe the set of algebraic bundles overX and algebraic structures on this set. Some applications to algebras generated by idempotents are suggested. 相似文献
10.
The solutions of the Nevanlinna-Pick interpolation problem for generalized Stieltjes matrix functions are parametrized via a fractional linear transformation over a subset of the class of classical Stieltjes functions. The fractional linear transformation of some of these functions may have a pole in one or more of the interpolation points, hence not all Stieltjes functions can serve as a parameter. The set of excluded parameters is characterized in terms of the two related Pick matrices.Dedicated to the memory of M. G. Kreîn 相似文献
11.
《Journal of Functional Analysis》2005,229(2):241-276
The Carathéodory problem in the N-variable non-commutative Herglotz-Agler class and the Carathéodory-Fejér problem in the N-variable non-commutative Schur-Agler class are posed. It is shown that the Carathéodory (resp., Carathéodory-Fejér) problem has a solution if and only if the non-commutative polynomial with given operator coefficients (the data of the problem indexed by an admissible set Λ) takes operator values with positive semidefinite real part (resp., contractive operator values) on N-tuples of Λ-jointly nilpotent contractive n×n matrices, for all n∈N. 相似文献
12.
13.
Gerard J. Murphy 《Integral Equations and Operator Theory》1997,27(2):221-227
The class of Toeplitz algebras associated to ordered groups is important in the analysis of Toeplitz operators on the generalised Hardy spaces defined by such groups. The conditions under which these Toeplitz algebras are Type I C*-algebras are investigated. 相似文献
14.
J. A. Ball Yu. I. Karlovich L. Rodman I. M. Spitkovsky 《Integral Equations and Operator Theory》1998,32(3):243-281
Sarason interpolation and Toeplitz corona problems are studied for almost periodic matrix functions. Recent results on almost periodic factorization and related generalized Toeplitz operators are the main tools in the study.Supported in part by NSF Grant DMS 9500912Supported in part by NATO Collaborative Research Grant 950332Supported by NSF Grant DMS 9500924 相似文献
15.
Timur Oikhberg 《Archiv der Mathematik》2006,86(4):356-364
We construct a “universal space” for 1-exact finite dimensional operator spaces (an analogue of the Gurarii space).
Received: 20 June 2005 相似文献
16.
17.
Stefano Serra 《Numerische Mathematik》1999,82(1):117-142
Preconditioned conjugate gradients (PCG) are widely and successfully used methods for solving a Toeplitz linear system [59,9,20,5,34,62,6,10,28,45,44,46,49]. Frobenius-optimal preconditioners are chosen in some proper matrix algebras and are
defined by minimizing the Frobenius distance from . The convergence features of these PCG have been naturally studied by means of the Weierstrass–Jackson Theorem [17,36,45],
owing to the profound relationship between the spectral features of the matrices , generated by the Fourier coefficients of a continuous function f, and the analytical properties of the symbol f itself. In this paper, we capsize this point of view by showing that the optimal preconditioners can be used to define both
new and just known linear positive operators uniformly approximating the function f. On the other hand, by modifying the Korovkin Theorem to study the Frobenius-optimal preconditioning problem, we provide
a new and unifying tool for analyzing all Frobenius-optimal preconditioners in any generic matrix algebra related to trigonometric
transforms. Finally, the multilevel case is sketched and discussed by showing that a Korovkin-type Theory also holds in a
multivariate sense.
Received October 1, 1996 / Revised version received May 7, 1998 相似文献
18.
A. N. Karapetyants V. S. Rabinovich N. L. Vasilevski 《Integral Equations and Operator Theory》2001,40(3):278-308
We describe the Fredholm symbol algebra for theC
*-algebra generated by two dimensional singular integral operators, acting onL
2(2), and whose symbols admit homogeneous discontinuities. Locally these discontinuities are modeled by homogeneous functions having slowly oscillating (and, in particular, piecewise continuous) discontinuities on a system of rays outgoing from the origin.These results extend the well-known Plamenevsky results for the two dimensional case. We present here an alternative and much clearer approach to the problem.Rostov State University RussiaPartially supported by Russian Fund for Fundamental Investigations, RFFI-98-01-01-023, and by CONACYT project 32424-EPartially supported by CONACYT Project 27934-E, México. 相似文献
19.
Konstantin M. Dyakonov 《Mathematische Annalen》2009,344(2):353-380
For a Toeplitz operator T
φ
, we study the interrelationship between smoothness properties of the symbol φ and those of the functions annihilated by T
φ
. For instance, it follows from our results that if φ is a unimodular function on the circle lying in some Lipschitz or Zygmund space Λα with 0 < α < ∞, and if f is an H
p
-function (p ≥ 1) with T
φ
f = 0, then f ∈ Λα and
for some c = c(α, p) and d = d(α, p); an explicit formula for the optimal exponent d is provided. Similar—and more general—results for various smoothness classes are obtained, and several approaches are discussed.
Furthermore, since a given non-null function f ∈ H
p
lies in the kernel of with , we derive information on the smoothness of H
p
-functions with smooth arguments. This can be viewed as a natural counterpart to the existing theory of analytic functions
with smooth moduli.
Supported in part by grants MTM2008-05561-C02-01/MTM, HF2006-0211 and MTM2007-30904-E from El Ministerio de Ciencia e Innovación
(Spain), and by grant 2005-SGR-00611 from DURSI (Generalitat de Catalunya). 相似文献
20.
Boris Freydin 《Integral Equations and Operator Theory》1997,29(2):211-230
Ball in [Ba] showed that the commutant lifting theorem for the nest algebras due to Paulsen and Power gives a unified approach to a wide class of interpolation problems for nest algebras. By restricting our attention to the case when nest algebras associated with the problems are discrete we derive a variant of the commutant lifting theorem which avoids language of representation theory and which is sufficient to treat an analog of the generalized Schur-Nevannlinna-Pick (SNP) problem in the setting of upper triangular operators. 相似文献