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981.
Yurij M. Berezansky 《Integral Equations and Operator Theory》2002,44(3):255-289
The article is devoted to two generalizations of the classical power moment problem, namely: 1) instead of representing the moment sequence by
n
, a representation by polynomialsP
n
(), 1, connected with a Jacobi matrix, appears; 2) in the representation, instead of
n
, the expression n
figures, where is a real generalized function (i.e., we investigate some infinite-dimensional moment problem).The work is partially supported by the DFG, Project 436 UKR 113/39/0 and by the CRDF, Project UM1-2090. 相似文献
982.
983.
In a category with injective hulls and a cogenerator, the embeddings into injective hulls can never form a natural transformation,
unless all objects are injective. In particular, assigning to a field its algebraic closure, to a poset or Boolean algebra
its Mac-Neille completion, and to an R-module its injective envelope is not functorial, if one wants the respective embeddings to form a natural transformation.
Received January 21, 2000; accepted in final form August 10, 2001.
RID="h1"
RID="h2"
RID="h3"
ID="h1"The hospitality of York University is gratefully acknowledged by the first author.
ID="h2"Third author partially supported by the Grant Agency of the Czech Republic under Grant no. 201/99/0310, and the hospitality
of York University is also acknowledged.
ID="h3"Partial financial assistance by the Natural Sciences and Engineering Councel of Canada is acknowledged by the fourth
author. 相似文献
984.
Small compact perturbation of strongly irreducible operators 总被引:4,自引:0,他引:4
An operatorT onH is called strongly irreducible ifT is not similar to any reducible operators. In this paper, we shall say yes to answer the following question raised by D. A. Herrero.Given an operatorT with connected spectrum (T) and a positive number , can we find a compact operatorK with K < such thatT+K is strongly irreducible?Supported by National Natural Science Foundation of China(19901011), Mathematical Center of State Education Commission of China and 973 Project of China 相似文献
985.
Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then exists in L
2-norm for any u, v∈L
∞(X, ℬ, μ). We also show that for A∈ℬ with μ(A)>0 one has . By the way of contrast, we bring examples showing that if measure preserving transformations T, S generate a solvable group, then (i) the above limits do not have to exist; (ii) the double recurrence property fails, that
is, for some A∈ℬ, μ(A)>0, one may have μ(A∩T
-n
A∩S
-
n
A)=0 for all n∈ℕ. Finally, we show that when T and S generate a nilpotent group of class ≤c, in L
2(X) for all u, v∈L
∞(X) if and only if T×S is ergodic on X×X and the group generated by T
-1
S, T
-2
S
2,..., T
-c
S
c
acts ergodically on X.
Oblatum 19-V-2000 & 5-VII-2001?Published online: 12 October 2001 相似文献
986.
D. S. Lubinsky 《Constructive Approximation》2002,18(2):285-308
Let a≥ 0 , ɛ >0 . We use potential theory to obtain a sharp lower bound for the linear Lebesgue measure of the set Here P is an arbitrary polynomial of degree ≤ n . We then apply this to diagonal and ray Padé sequences for functions analytic (or meromorphic) in the unit ball. For example,
we show that the diagonal \left{ [n/n]\right}
n=1
∞
sequence provides good approximation on almost one-eighth of the circles centre 0 , and the \left{ [2n/n]\right}
n=1
∞
sequence on almost one-quarter of such circles.
July 18, 2000. Date revised: . Date accepted: April 19, 2001. 相似文献
987.
Let E\subset \Bbb R
s
be compact and let d
n
E
denote the dimension of the space of polynomials of degree at most n in s variables restricted to E . We introduce the notion of an asymptotic interpolation measure (AIM). Such a measure, if it exists , describes the asymptotic behavior of any scheme τ
n
={ \bf x
k,n
}
k=1
dnE
, n=1,2,\ldots , of nodes for multivariate polynomial interpolation for which the norms of the corresponding interpolation operators do
not grow geometrically large with n . We demonstrate the existence of AIMs for the finite union of compact subsets of certain algebraic curves in R
2
. It turns out that the theory of logarithmic potentials with external fields plays a useful role in the investigation. Furthermore,
for the sets mentioned above, we give a computationally simple construction for ``good' interpolation schemes.
November 9, 2000. Date revised: August 4, 2001. Date accepted: September 14, 2001. 相似文献
988.
In this paper we give the precise index growth for the embedded hypersurfaces of revolution with constant mean curvature
(cmc) 1 in (Delaunay unduloids). When n=3, using the asymptotics result of Korevaar, Kusner and Solomon, we derive an explicit asymptotic index growth rate for finite
topology cmc 1 surfaces with properly embedded ends. Similar results are obtained for hypersurfaces with cmc bigger than 1
in hyperbolic space.
Received: 6 July 2000; in final form: 10 September 2000 / Published online: 25 June 2001 相似文献
989.
We study biorthogonal bases of compactly supported wavelets constructed from box splines in ℝ
N
with any integer dilation factor. For a suitable class of box splines we write explicitly dual low-pass filters of arbitrarily
high regularity and indicate how to construct the corresponding high-pass filters (primal and dual).
Received: August 23, 2000; in final form: March 10, 2001?Published online: May 29, 2002 相似文献
990.
Summary. We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms.
Received March 28, 2000 / Revised version received June 23, 2000 / Published online March 8, 2002
RID="*"
ID="*" Supported by the National Science Foundation under grant DMS-9870187
RID="**"
ID="**" Supported by the National Science Foundation under grant DMS-9803340 and by the Army Research Office under grant DAAD-19-99-1-0160 相似文献