共查询到20条相似文献,搜索用时 656 毫秒
1.
A. V. Kroo 《Mathematical Notes》1977,22(1):536-546
Suppose thatk, rz+, W
o
r
H[]C= {ff is a 2-periodic function,f Cr [–, ], (f(r), ) ()}, Tk is the space of trigonometric polynomials of order k, pk(f)Tk is the polynomial of best uniform approximation to f, and Ek(f) is the error of the best approximation. It is shown that for an arbitrary > 0 we have,where for 0<⩽(1),k > 0.R () is the root of the equation
, and for k = 0 or > (1) we have R()=.Translated from Matematicheskie Zametki, Vol. 22, No. 1, pp. 85–101, July, 1977.The author thanks S. B. Stechkin for posing the problem and for his attention to this work. 相似文献
2.
W. Hazod 《Probability Theory and Related Fields》1971,20(4):259-270
Ohne ZusammenfassungBezeichnungen und Symbole
G
lokalkompakte topologische Gruppe
-
M(G)/R(G)/P(G)/
regulÄre komplexe/reelle/positive Ma\e/
-
Q(G)/W(G)
Ma\e mit · l/Wahrscheinlichkeitsma\e
-
x
Punktma\:
x(f)=f(x)
-
v
Faltung,
— Bekanntlich bildet M(G) bezüglich der Faltung eine Banachalgebra;
-
Involution in M(G),
, wobei — die Komplexkonjugierte bezeichnet
- ×
diskreter Anteil eines Ma\es,
-
T
gm
Faltungsoperator auf L
2 (G) (bezüglich des linken Haarschen Ma\es),
f.ü.
-
p(·)/q(·)/u(·)
- exp(·.)
Exponentialfunktion, exp
- normal/unitÄr/symmetrisch/positiv definit
bezeichnet man ein Ma\ , wenn der Faltungsoperator T
diese Eigenschaft besitzt
- invertierbar
hei\t
M(G), wenn ein vM(G) existiert, so da\ v = v=
e
-
1/n
n-te Wurzel von
1
hei\t wenn(
1/n)n=
1
-
1 hei\t unendlich teilbar
wenn zu jedem natürlichen n eine n-te Wurzel
1/n von existiert
-
N
Menge der natürlichen Zahlen 相似文献
3.
Let |E(G)|= andf, a 1-1 mapping ofV(G) into {0,1,...,}. Thenf is called a -valuation ofG if the induced function given by
, for alluvE(G) is 1-1. A -valuationf is called an -valuation ofG if there exists a nonnegative number such that for everyuvE(G) withf(u)<f(v),f(u)<f(v). Let
denote the graph of then-dimensionalG-cube. ForG=K
3, 3,K
4, 4, andP
k
,it is shown that for any positive integern, then-dimensionalG-cube has an -valuation. This gives rise to decompositions of some complete graphs into certain bipartite graphs. 相似文献
4.
Gerhard Opfer 《Numerische Mathematik》1979,32(4):423-429
Summary It is well known that for a given simply connected regionR containing zero the uniform norm
attains its minimum in the class of all holomorphic functions normalized byf(0)=0 andf(0)=1 only for the conformal mappingfRD(r)={z|z|}. It is shown that this theorem is still valid if one replaces the ordinary modulus | | on by any other norm on . For instance it is possible to obtain direct mappings ofR onto parallelograms, rectangles and ellipses. For the special norms |1 and | this leads to a simple and fast computational technique involving linear programming methods. Several numerical examples are given. 相似文献
5.
6.
Bohdan Zelinka 《Czechoslovak Mathematical Journal》2001,51(2):225-229
The signed total domination number of a graph is a certain variant of the domination number. If is a vertex of a graph G, then N() is its oper neighbourhood, i.e. the set of all vertices adjacent to in G. A mapping f: V(G)-1, 1, where V(G) is the vertex set of G, is called a signed total dominating function (STDF) on G, if
for each
V(G). The minimum of values
, taken over all STDF's of G, is called the signed total domination number of G and denoted by st(G). A theorem stating lower bounds for st(G) is stated for the case of regular graphs. The values of this number are found for complete graphs, circuits, complete bipartite graphs and graphs on n-side prisms. At the end it is proved that st(G) is not bounded from below in general. 相似文献
7.
Victor Kaftal 《Integral Equations and Operator Theory》1982,5(1):50-70
LetA be a von Neumann algebra,J be the ideal of compact operators relative toA and letF
+ be the left-Fredholm class ofA. We call almost left-Fredholm the class
= {A A: if P A is a projection and AP J then P J}. Then
and the inclusion is proper unlessA is semifinite and has a non-large center.
satisfies all of the algebraic properties ofF
+ but it is generally not open. IfA is semifinite then A
iff there are central projectionsG
with G = I such that AG F+(AG). Let :A A/J. Then the left almost essential spectrum ofA A,
, coincides with the set of eigenvalues of (A) 相似文献
8.
Matching Polynomials And Duality 总被引:2,自引:0,他引:2
Let G be a simple graph on n vertices. An r-matching in G is a set of r independent edges. The number of r-matchings in G will be denoted by p(G, r). We set p(G, 0) = 1 and define the matching polynomial of G by
and the signless matching polynomial of G by
.It is classical that the matching polynomials of a graph G determine the matching polynomials of its complement
. We make this statement more explicit by proving new duality theorems by the generating function method for set functions. In particular, we show that the matching functions
and
are, up to a sign, real Fourier transforms of each other.Moreover, we generalize Foatas combinatorial proof of the Mehler formula for Hermite polynomials to matching polynomials. This provides a new short proof of the classical fact that all zeros of µ(G, x) are real. The same statement is also proved for a common generalization of the matching polynomial and the rook polynomial. 相似文献
9.
G. A. Kalyabin 《Functional Analysis and Its Applications》2004,38(3):184-191
We solve Tikhomirov's problem on the explicit computation of sharp constants in the Kolmogorov type inequalities
Specifically, we prove that
for all and k{0,...,n-1}. We establish symmetry and regularity properties of the numbers A
n,k
and study their asymptotic behavior as n for the cases k=O(n
2/3) and k/n(0,1).Similar problems were previously studied by Gabushin and Taikov. 相似文献
10.
K. Sikorski 《Numerische Mathematik》1984,43(2):225-240
Summary For a given nonnegative we seek a pointx
* such that |f(x
*)| wheref is a nonlinear transformation of the cubeB=[0,1]
m
into (or
p
,p>1) satisfying a Lipschitz condition with the constantK and having a zero inB.The information operator onf consists ofn values of arbitrary linear functionals which are computed adaptively. The pointx
* is constructed by means of an algorithm which is a mapping depending on the information operator. We find an optimal algorithm, i.e., algorithm with the smallest error, which usesn function evaluations computed adaptively. We also exhibit nearly optimal information operators, i.e., the linear functionals for which the error of an optimal algorithm that uses them is almost minimal. Nearly optimal information operators consists ofn nonadaptive function evaluations at equispaced pointsx
j
in the cubeB. This result exhibits the superiority of the T. Aird and J. Rice procedure ZSRCH (IMSL library [1]) over Sobol's approach [7] for solving nonlinear equations in our class of functions. We also prove that the simple search algorithm which yields a pointx
*=x
k
such that
is nearly optimal. The complexity, i.e., the minimal cost of solving our problem is roughly equal to (K/)
m
. 相似文献
11.
Winfried Just 《Algebra Universalis》1985,20(2):135-142
In this paper we show that the following is relatively consistent withZFC +CH: There is no superatomic Boolean algebra of height 2+1 and width, and there is no superatomic Boolean algebraA with
for 0<<1 and
Presented by J. Mycielski. 相似文献
12.
O. L. Vinogradov 《Journal of Mathematical Sciences》2003,114(5):1608-1627
Let
be the space of 2-periodic functions whose (r – 1)th-order derivative is absolutely continuous on any segment and rth-order derivative belongs to L
p, S
2n,m
is the space of 2-periodic splines of order m of minimal defect over the uniform partition
. In this paper, we construct linear operators
such that
where
To construct the operators X
n,r,m, we use the same idea as in the polynomial case, i.e., the interpolation of Bernoulli kernels. As is proved, the operators X
n,r,m converge to polynomial Akhiezer–Krein–Favard operators as
. Bibliography: 10 titles. 相似文献
13.
F. G. Abdullayev 《Czechoslovak Mathematical Journal》2001,51(3):643-660
Let C be the extended complex plane; G C a finite Jordan with 0 G; w= (z) the conformal mapping of G onto the disk
normalized by
. Let us set
, and let
be the generalized Bieberbach polynomial of degree n for the pair (G,0), which minimizes the integral
in the class of all polynomials of degree not exceeding n with
. In this paper we study the uniform convergence of the generalized Bieberbach polynomials
with interior and exterior zero angles and determine its dependence on the properties of boundary arcs and the degree of their tangency. 相似文献
14.
Piotr Kot 《Czechoslovak Mathematical Journal》2004,54(1):55-63
For z B
n, the boundary of the unit ball in
. If
the exceptional set for f. In this note we give a tool for describing such sets. Moreover we prove that if Eis a G
and F
subset of the projective (n– 1)-dimensional space
then there exists a holomorphic function fin the unit ball B
nso that E(f) = E. 相似文献
15.
Let
be a nondecreasing sequence of positive numbers and let l
1,α be the space of real sequences
for which
. We associate every sequence ξ from l
1,α with a sequence
, where ϕ(·) is a permutation of the natural series such that
, j ∈ ℕ. If p is a bounded seminorm on l
1,α and
, then
Using this equality, we obtain several known statements.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 1002–1006, July, 2005. 相似文献
16.
On the Range of the Aluthge Transform 总被引:1,自引:0,他引:1
Let
be the algebra of all bounded linear operators on a complex separable Hilbert space
For an operator
let
be the Aluthge transform of T and we define
for all
where T = U|T| is a polar decomposition of T. In this short note, we consider an elementary property of the range
of Δ. We prove that R(Δ) is neither closed nor dense in
However R(Δ) is strongly dense if
is infinite dimensional.
An erratum to this article is available at . 相似文献
17.
We prove that if is the error of a simple quadrature formula and ω(ε, δ)1 is the integral modulus of continuity, then, for any δ ≥/π andn,r = 1, 2, …, the following equality is true: whereD
r
is the Bernoulli kernel. 相似文献
18.
G. Akrivis 《Numerische Mathematik》1984,44(2):261-278
Summary We consider Gauss quadrature formulaeQ
n
,n, approximating the integral
,w an even weight function. Let
be analytic inK
r
:={z:|z|<r},r>1, and
. The error functionalR
n
:=I-Q
n
is continuous with respect to |·|r and the relation
, q2k
(x):=x
2k
holds.In this paper estimates for R
n
are given. To this end we first derive two new representations of R
n
which are essential for our further investigations. The R
n
=r
2
R
n
(), with (x):=1/(r
2-x
2), is estimated in various ways by using the best uniform approximation of in P2n-1, and also the expansion of with respect to Chebyshe polynomials of the first and second kind. Forw(x)=(1-x
2), =±1/2, R
n
is calculated. The asymptotic behaviour, forr1+, of R
n
and of the derived error bounds is also discussed. Finally, we compare different error bounds and give numerical examples. 相似文献
19.
Eike Born 《Journal of Theoretical Probability》1989,2(3):325-342
LetG be a locally compact group and (t)t 0 a continuous convolution semigroup of probability measures onG. We show that an operatorN is the infinitesimal generator of (t)t 0 iffN is defined at least on the spaceC
2(G) of twice right differentiable functions and if
相似文献
20.
We establish a criterion for the existence of a solution of the interpolation problem f(
n
) = b
n in the class of functions f analytic in the unit disk and satisfying the relation
|