共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
B. Yousefi 《Czechoslovak Mathematical Journal》2004,54(1):261-266
Let
be a sequence of positive numbers and 1 p< . We consider the space H
p() of all power series
such that
. We investigate strict cyclicity of
the weakly closed algebra generated by the operator of multiplication by zacting on H
p(), and determine the maximal ideal space, the dual space and the reflexivity of the algebra
. We also give a necessary condition for a composition operator to be bounded on H
p() when
is strictly cyclic. 相似文献
3.
Let
be realhomogeneous functions in
ofdegree
and let bethe Borel measure on
given by
where dx denotes theLebesgue measure on
and > 0. Let T
be the convolution operator
and let
Assume that, for x 0, the followingtwo conditions hold:
vanishes only at h = 0 and
. In this paper we show that if
then E
is the empty set and if
then E
is the closed segment withendpoints
and
. Also, we give some examples. 相似文献
4.
Suppose that
is an arbitrary finite complex Borel measure on the interval
is its Poisson integral,
and
are the conjugate harmonics of
, and
is the nontangential limiting value of the analytic function
as
. In this paper, we consider the problem of representing the analytic function
in terms of its boundary values
. 相似文献
5.
H. P. A. Künzi S. Romaguera M. A. Sánchez-Granero 《Czechoslovak Mathematical Journal》2004,54(1):215-228
We characterize those Tychonoff quasi-uniform spaces
for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family
of nonempty compact subsets of X. We deduce, among other results, that the Hausdorff-Bourbaki quasi-uniformity of the locally finite quasi-uniformity of a Tychonoff space Xis uniformly locally compact on
if and only if Xis paracompact and locally compact. We also introduce the notion of a co-uniformly locally compact quasi-uniform space and show that a Hausdorff topological space is -compact if and only if its (lower) semi-continuous quasi-uniformity is co-uniformly locally compact. A characterization of those Hausdorff quasi-uniform spaces
for which the Hausdorff-Bourbaki quasi-uniformity is co-uniformly locally compact on
is obtained. 相似文献
6.
Márcia Federson 《Czechoslovak Mathematical Journal》2002,52(2):429-437
We prove two versions of the Monotone Convergence Theorem for the vector integral of Kurzweil,
, where R is a compact interval of
, and f are functions with values on L(Z,W) and Z respectively, and Z and W are monotone ordered normed spaces. Analogous results can be obtained for the Kurzweil vector integral,
, as well as to unbounded intervals R. 相似文献
7.
Adhemar Bultheel Pablo González-Vera Erik Hendriksen Olav Njåstad 《Acta Appl Math》2000,61(1-3):101-118
From the Erds–Turán theorem, it is known that if f is a continuous function on
and L
n
(f, z) denotes the unique Laurent polynomial interpolating f at the (2 n + 1)th roots of unity, then
Several years later, Walsh and Sharma produced similar result but taking into consideration a function analytic in
and continuous on
and making use of algebraic interpolating polynomials in the roots of unity.In this paper, the above results will be generalized in two directions. On the one hand, more general rational functions than polynomials or Laurent polynomials will be used as interpolants and, on the other hand, the interpolation points will be zeros of certain para-orthogonal functions with respect to a given measure on
. 相似文献
8.
Zdzislaw Brzezniak Szymon Peszat Jerzy Zabczyk 《Czechoslovak Mathematical Journal》2001,51(4):679-684
Let B be a Brownian motion, and let
be the space of all continuous periodic functions f with period 1. It is shown that the set of all f
such that the stochastic convolution
does not have a modification with bounded trajectories, and consequently does not have a continuous modification, is of the second Baire category. 相似文献
9.
Let X be an open subset of
n and (f1, ...,fp): X
p be a holomorphic mapping. We prove that if (x0,0, 0) T* ×
p does not belong to the characteristic variety of the
X []-module
X[]f, then there exists a conic neighborhood V × of (x0, 0) such the function
is rapidely decreasing in | Im | for with Re bounded, for any (n,n)-form of class C with compact support in V. The following partial converse of this result is also established: if
for all (n,n)-forms of class C with compact support in X, then
. 相似文献
10.
We consider second-order subelliptic operators with complex coefficients over a connected Lie group G. If the principal coefficients are right uniformly continuous then we prove that the operators generate strongly continuous holomorphic semigroups with kernels K satisfying Gaussian bounds. Moreover, the kernels are Hölder continuous and for each 0, 1 and > 0 one has estimates
for g, h, k, l G and all z in a subsector of the sector of holomorphy with
where
denotes the canonical subelliptic modulus and D " the local dimension.These results are established by a blend of elliptic and parabolic techniques in which De Giorgi estimates and Morrey–Campanato spaces play an important role. 相似文献
11.
C. S. Lin 《Czechoslovak Mathematical Journal》2002,52(3):665-672
In this paper we prove two results. The first is an extension of the result of G. D. Jones [4[:Every nontrivial solution for
must be unbounded, provided
, in
and for every bounded subset I, f(t, z) is bounded in E × I.(B) Every bounded solution for
, in
, must be constant, provided
in
and for every bounded subset I,
is bounded in
. 相似文献
12.
Polynomial Approximations on a Family of Two Segments 总被引:1,自引:1,他引:0
Introduce the notation:
,is the union of two segments [- 1,1] and
is the Holder class with exponent on
is the Green function of the set
with a logarithmic pole at infinity,
0,\rho _h (z,\varepsilon ) = {\text{dist(}}z,L_h (\varepsilon ))$$
" align="middle" border="0">
. We prove the following result: There exist positive constants b()and a() depending only on such that if
then
.Bibliography: 3 titles. 相似文献
13.
Sjoerd E. Crans 《K-Theory》2003,28(1):39-105
Let
be n-dimensional teisi, i.e., higher-dimensional Gray-categorical structures. The following questions can be asked. Does a left q-transfor
, i.e., a functor 2
q
, induce a right q-transfor
, i.e., a functor
More generally, does a functor
induce a functor
For k-arrows c and
whose (k – 1)-sources and targets agree, does a q-transfor
induce a q-transfor
, for appropriate k-arrows
For k-arrows c and
whose (k – 1)-sources and targets agree, does a q-transfor
induce a (q + k + 1)-transfor
, for appropriate k-arrows
I give answers to these questions in the cases where n-dimensional teisi and their tensor product have been defined, i.e., for n 3, and for n up to 5 in some cases that do not need all data and axioms of n-dimensional teisi.I apply the above to compositions in teisi, in particular to braidings and syllepses. One of the results is that a braiding on a monoidal 2-category induces a pseudo-natural transformation
, where
is the reverse of ? –, which is almost, but not quite, equal to – ?. However, in higher dimensions need not be reversible, so a braiding on a higher-dimensional tas can not be seen as a transfor A B B A. 相似文献
14.
On Kolmogorov-Type Inequalities Taking into Account the Number of Changes in the Sign of Derivatives
For 2-periodic functions
and arbitrary q [1, ] and p (0, ], we obtain the new exact Kolmogorov-type inequality
which takes into account the number of changes in the sign of the derivatives (x
(k)) over the period. Here, = (r – k + 1/q)/(r + 1/p),
r
is the Euler perfect spline of degree r,
and
. The inequality indicated turns into the equality for functions of the form x(t) = a
r
(nt + b), a, b R, n N. We also obtain an analog of this inequality in the case where k = 0 and q = and prove new exact Bernstein-type inequalities for trigonometric polynomials and splines. 相似文献
15.
Gerald Kuba 《Acta Mathematica Hungarica》2002,95(1-2):115-124
For a positive real parameter t, real numbers , , and
, we consider sums
, where
is the rounding error function, i.e.\
. Generalizing and improving the main result of Part I of the paper we show that there exists an absolute constant
such that
for all
, and all
. Further, we give applications concerning the circle problem with linear, polynomial, and general weight. 相似文献
16.
Marian Nowak 《Czechoslovak Mathematical Journal》2000,50(2):401-414
Let
be a real Banach space and let E be an ideal of L
0 over a -finite measure space (, , ). Let (X) be the space of all strongly -measurable functions f: X such that the scalar function
, defined by
, belongs to E. The paper deals with strong topologies on E(X). In particular, the strong topology
the order continuous dual of E(X)) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies. 相似文献
17.
Let P
k be a path on k vertices. In an earlier paper we have proved that each polyhedral map G on any compact 2-manifold
with Euler characteristic
contains a path P
k such that each vertex of this path has, in G, degree
. Moreover, this bound is attained for k = 1 or k 2, k even. In this paper we prove that for each odd
, this bound is the best possible on infinitely many compact 2-manifolds, but on infinitely many other compact 2-manifolds the upper bound can be lowered to
. 相似文献
18.
The paper is concerned with oscillation properties of n-th order neutral differential equations of the form
where c is a real number with
with (t) < t and
.Sufficient conditions are established for the existence of positive solutions and for oscillation of bounded solutions of the above equation. Combination of these conditions provides necessary and sufficient conditions for oscillation of bounded solutions of the equation. Furthermore, the results are generalized to equations in which c is a function of t and a certain type of a forcing term is present. 相似文献
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19.
In this article, we consider the operator L defined by the differential expression
in L
2(–, ), where q is a complex valued function. Discussing the spectrum, we prove that L has a finite number of eigenvalues and spectral singularities, if the condition
holds. Later we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities. 相似文献
20.
We prove that the maximal isoperimetric function on a Riemannian manifold of conformally hyperbolic type can be reduced to the linear canonical form P(x) = x by a conformal change of the Riemannian metric. In other words, the isoperimetric inequality
, relating the volume V(D) of a domain D to the area
of its boundary, can be reduced to the form
, known for the Lobachevskii hyperbolic space. 相似文献