共查询到20条相似文献,搜索用时 31 毫秒
1.
A. B. J. Kuijlaars 《Constructive Approximation》2000,16(4):559-589
We consider the asymptotic zero behavior of polynomials that are extremal with respect to slowly decaying weights on [0, ∈fty) , such as the log-normal weight \exp(-γ
2
log
2
x) . The zeros are contracted by taking the appropriate d
n
th roots with d
n
→∈fty . The limiting distribution of the contracted zeros is described in terms of the solution of an extremal problem in logarithmic
potential theory with a circular symmetric external field.
November 23, 1998. Date revised: February 8, 1999. Date accepted: March 2, 1999. 相似文献
2.
We give a strong converse inequality of type A in the usual sup-norm for a noncentered gamma operator L
t
*
, providing at the same time upper and lower constants. This operator, which does not preserve smooth functions, is connected
with real Laplace transforms and Poisson mixtures. We use a probabilistic approach based on the representation of L
t
*
in terms of gamma processes.
October 15, 1997. Date revised: September 14, 1998. Date accepted: October 7, 1998. 相似文献
3.
We extend the results of Pollard [4] and give asymptotic estimates for the norm of the Fourier—Gegenbauer projection operator
in the appropriate weighted L
p
space. In particular, we settle the question of whether the projection is bounded for p=(2λ+1)/λ and p=(2λ+1)/(λ+1) , where λ is the index for the family of Gegenbauer polynomials under consideration.
March 19, 1997. Date revised: June 3, 1998. Date accepted: August 1, 1998. 相似文献
4.
This paper deals with the spectral problems for high-order nonsymmetric difference operators. The method of investigation
is based on the analysis of the genetic sums formulas for the moments of the operator. The parameters of these sums are shown
to be connected with coefficients of the introduced vector Stieltjes continued fraction. The connections with vector orthogonality,
Hermite—Padé approximation, and Hankel determinants are investigated. This gives a tool for the analysis of the solution of
the direct and inverse spectral problem of the operator. It is applied to the integration of hierarchy of the discrete KdV
equations. The existence of a global solution is proved.
July 13, 1998. Date revised: July 12, 1999. Date accepted: July 26, 1999. 相似文献
5.
We show that for a broad class of interpolatory matrices on [-1,1] the sequence of polynomials induced by Hermite—Fejér interpolation to f(z)=z diverges everywhere in the complex plane outside the interval of interpolation [-1,1] . This result is in striking contrast to the behavior of the Lagrange interpolating polynomials.
June 15, 1998. Date accepted: January 26, 1999. 相似文献
6.
M. Reimer 《Constructive Approximation》2002,18(2):183-204
Hyperinterpolation on the sphere, as introduced by Sloan in 1995, is a constructive approximation method which is favorable
in comparison with interpolation, but still lacking in pointwise convergence in the uniform norm. For this reason we combine
the idea of hyperinterpolation and of summation in a concept of generalized hyperinterpolation. This is no longer projectory,
but convergent if a matrix method A is used which satisfies some assumptions. Especially we study A partial sums which are defined by some singular integral used by Newman and Shapiro in 1964 to derive a Jackson-type inequality
on the sphere. We could prove in 1999 that this inequality is realized even by the corresponding discrete operators, which
are generalized hyperinterpolation operators. In view of this result the Newman—Shapiro operators themselves gain new attention.
Actually, in their case, A furnishes second-order approximation, which is best possible for positive operators. As an application we discuss a method
for tomography, which reconstructs smooth and nonsmooth components at their adequate rate of convergence. However, it is an
open question how second-order results can be obtained in the discrete case, this means in generalized hyperinterpolation
itself, if results of this kind are possible at all.
March 9, 2000. Date revised: October 2, 2000. Date accepted: March 8, 2001. 相似文献
7.
D. S. Lubinsky 《Constructive Approximation》1999,15(4):577-610
We obtain converse Marcinkiewicz—Zygmund inequalities such as
for polynomials P of degree ≤ n-1 , under general conditions on the points {t
j
}
n
j=1
and on the function ν . The weights {μ
j
}
n
j=1
are appropriately chosen. We illustrate the results by applying them to extended Lagrange interpolation for exponential
weights on [-1,1] .
December 3, 1997. Date revised: December 7, 1998. Date accepted: January 8, 1999. 相似文献
8.
Regularity of Multivariate Refinable Functions 总被引:1,自引:0,他引:1
The regularity of a univariate compactly supported refinable function is known to be related to the spectral properties of
an associated transfer operator. In the case of multivariate refinable functions with a general dilation matrix A , although factorization techniques, which are typically used in the univariate setting, are no longer applicable, we derive
similar results that also depend on the spectral properties of A .
September 30, 1996. Dates revised: December 1, 1996; February 14, 1997; August 1, 1997; November 11, 1997. Date accepted:
November 14, 1997. 相似文献
9.
T. Bloom 《Constructive Approximation》2001,17(1):91-102
Let {r
n
} be a sequence of rational functions deg( r
n
≤ n) that converge rapidly in measure to an analytic function f on an open set in C
N
. We show that {r
n
} converges rapidly in capacity to f on its natural domain of definition W
f
(which, by a result of Goncar, is an open subset of C
N
).
In particular, for f meromorphic on C
N
and analytic near zero the sequence of Padé approximants {π
n
(z, f, λ)} (as defined by Goncar) converges rapidly in capacity to f on C
N
.
January 14, 1999. Date revised: October 7, 1999. Date accepted: November 1, 1999. 相似文献
10.
An extremal problem for the coefficients of sine polynomials, which are nonnegative in [0,π] , posed and discussed by Rogosinski and Szegő is under consideration. An analog of the Fejér—Riesz representation of nonnegative
general trigonometric and cosine polynomials is proved for nonnegative sine polynomials. Various extremal sine polynomials
for the problem of Rogosinski and Szegő are obtained explicitly. Associated cosine polynomials k
n
(θ) are constructed in such a way that { k
n
(θ) } are summability kernels. Thus, the L
p
, pointwise and almost everywhere convergence of the corresponding convolutions, is established.
April 26, 2000. Date revised: December 28, 2000. Date accepted: February 8, 2001. 相似文献
11.
We study a 22 operator matrix associated with a closed densely
defined operator. Among others, the selfadjointness of a closed symmetric
operator and the strong commutativity of two (unbounded) self-adjoint operators
are characterized in terms of the related operator matrices. We propose
a definition of strong commutativity for closed symmetric operators.
Submitted: November 8, 2001 相似文献
12.
Sherwin Kouchekian 《Integral Equations and Operator Theory》2003,45(3):319-342
The unbounded Bergman operator, the operator of multiplication
by on an unbounded open subset of the plane, is considered. We give a complete
answer regarding the density problem of unbounded Bergman operators
in terms of its equivalence to the problem of bounded point evaluations for the
Bergman spaces. Using this equivalence and the notion of Wiener capacity, we
obtain simple geometric conditions that classify almost those open subsets of
the plane for which the corresponding Bergman operators are densely defined.
With the aid of an analytic approach, we are also able to give condition for a
large collection of open subsets of the plane for which all the positive integer
powers of the corresponding Bergman operators are densely defined.
Submitted: December 14, 2001? Revised: January 14, 2001. 相似文献
13.
H. Volkmer 《Constructive Approximation》1999,15(4):467-480
It is shown that products of polynomials introduced by Heine and Stieltjes form orthogonal bases in suitable function spaces.
A theorem on the expansion of analytic function in these bases is proved.
June 5, 1997. Date revised: November 18, 1997. Date accepted: January 14, 1998. 相似文献
14.
L
&
∞ bounds for norms of projections onto bivariate polynomial spline spaces on regular triangulations with stable local bases
are established. The general results are then applied to obtain error bounds for best L
2
- and l
2
-approximation by splines on quasi-uniform triangulations.
March 8, 2000. Date revised: November 20, 2000. Date accepted: July 9, 2001. 相似文献
15.
A second look at the authors' [BDR1], [BDR2] characterization of the approximation order of a Finitely generated Shift-Invariant
subspace S(Φ) of L
2
(R
d
) results in a more explicit formulation entirely in terms of the (Fourier transform of the) generators of the subspace. Further, when the generators satisfy a certain technical condition, then, under the mild assumption that
the set of 1-periodizations of the generators is linearly independent, such a space is shown to provide approximation order
k if and only if contains a ψ (necessarily unique) satisfying . The technical condition is satisfied, e.g., when the generators are at infinity for some ρ>k+d . In the case of compactly supported generators, this recovers an earlier result of Jia [J1], [J2].
March 19. 1996. Date revised: September 6, 1996. 相似文献
16.
It is shown that the m th-order derivative of the n th-order Bernstein polynomial of a function f satisfying a certain Lipschitz condition, can be written for n\rightarrow +∈fty as a singular integral of Gauss—Weierstrass type, m times differentiated (in a certain sense) under the integral sign. The theorem is applied to yield an overdifferentiation formula, involving p times differentiated Bernstein polynomials of functions that are not C
p
.
December 1, 1998. Dates revised: July 22, 1999 and January 11, 2000. Date accepted: February 1, 2000. 相似文献
17.
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
18.
Lanzhe Liu 《Proceedings Mathematical Sciences》2004,114(3):235-251
In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue
spaces to Orlicz spaces are obtained. The operators include Calderón—Zygmund singular integral operator, fractional integral
operator, Littlewood—Paley operator and Marcinkiewicz operator. 相似文献
19.
An infinite asymptotic expansion is derived for the Meixner—Pollaczek polynomials M
n
(nα;δ, η) as n→∞ , which holds uniformly for -M≤α≤ M , where M can be any positive number. This expansion involves the parabolic cylinder function and its derivative. If α
n, s
denotes the s th zero of M
n
(nα;δ, η) , counted from the right, and if α˜
n,s
denotes its s th zero counted from the left, then for each fixed s , three-term asymptotic approximations are obtained for both α
n,s
and α˜
n,s
as n→∞ .
December 28, 1998. Date revised: June 4, 1999. Date accepted: September 6, 1999. 相似文献
20.
For certain classes of fractal differential equations on the Sierpinski gasket, built using the Kigami Laplacian, we describe
how to approximate solutions using the finite element method based on piecewise harmonic or piecewise biharmonic splines.
We give theoretical error estimates, and compare these with experimental data obtained using a computer implementation of
the method (available at the web site http://mathlab.cit.cornell.edu/\sim gibbons). We also explain some interesting structure concerning the spectrum of the Laplacian that became apparent from the
experimental data.
March 29, 2000. Date revised: March 6, 2001. Date accepted: March 21, 2001. 相似文献