共查询到20条相似文献,搜索用时 15 毫秒
1.
We obtain asymptotic equalities for the upper bounds of approximations by interpolation trigonometric polynomials on classes of convolutions of periodic functions admitting a regular extension to a fixed strip of the complex plane. 相似文献
2.
F. Bazsó 《Acta Mathematica Hungarica》2000,87(3):197-203
The notion of Jacobi matrix is introduced for B
m
B
n
mappings. The chain rule, the inverse function theorem and the implicit function theorem are proved. The meaning of functional dependence in the context of Boolean functions is discussed. Parallel is drawn with usual calculus. 相似文献
3.
Hermann Knig 《Mathematische Nachrichten》1991,152(1):215-227
We study the decay of the Fourier-coefficients of vector-valued functions F : T → X, X a Banach space. Differentiable functions f generally have absolutely summable Fourier-coefficients, f (n) <, iff X is K-convex. More precise statements on the decay of f (n) for regular functions f can be given if X has Fourier-type p. If f belongs to the Besov space, the sequence (||f(n)||) belongs to the Lorentz sequence space lt,v with 1/t = λ + 1/max (u′, p′). This result is the best possible in the vector-valued case and generalizes the well-known scalar results. 相似文献
4.
Stefan Cobzaş 《Acta Appl Math》2004,80(3):363-363
5.
M. Freund 《Results in Mathematics》1988,13(1-2):81-98
The rate of best polynomial approximation of an analytic function on a compact Faber set K is characterized in terms of the rate of growth of its Faber coefficients and compared with the rate of approximation by the partial sums of the Faber series. Also the convergence of sequences of interpolating polynomials constructed for various systems of nodes is studied by considering the growth of the interpolated function. Under appropriate assumptions on K the approximation by interpolating polynomials can be incorporated in the characterization theorem. Emphasis is laid on high precision in describing the rate of approximation and on admitting a large class of functions. 相似文献
6.
7.
Christopher Boyd 《Czechoslovak Mathematical Journal》2003,53(2):365-376
For U a balanced open subset of a Fréchet space E and F a dual-Banach space we introduce the topology on the space
of holomorphic functions from U into F. This topology allows us to construct a predual for
which in turn allows us to investigate the topological structure of spaces of vector-valued holomorphic functions. In particular, we are able to give necessary and sufficient conditions for the equivalence and compatibility of various topologies on spaces of vector-valued holomorphic functions. 相似文献
8.
We characterize composition operators on spaces of real analyticfunctions which at the same time have closed image and are openonto their images. Under some mild assumptions, we also characterizecomposition operators with closed range and composition operatorsopen onto their images. 2000 Mathematics Subject Classification46E10, 47B33, 32C07 (primary), 26E05, 32E30, 32D15 (secondary). 相似文献
9.
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
where : [1; +) (0; +) is an increasing function such that the function ln(t) is convex with respect to lnt on the interval [1; +) and lnt = o(ln(t)), t . 相似文献
10.
V. L. Sharan 《Journal of Mathematical Sciences》2001,107(1):3601-3603
A new criterion of solvability of the interpolation problem f(
n
)=bn in the class of functions f, analytic in the right half-plane
and such that there exists c
1(0;+) such that |f(z)|c
1exp((c1|z|)) for all z
, where is a positive increasing continuous differentiable function on [0;+), for which (t)+ as t+ and there exists c
2(0;+) such that
for all t 1 is described. 相似文献
11.
12.
Smirnov domains with non-smooth boundaries do admit non-trivial functions of Smirnov class with real boundary values. We will show that the existance of functions in Smirnov classes with real boundary values is directly dependent on the boundary characteristics of a Smirnov domain. 相似文献
13.
N. Dinh M. A. Goberna M. A. López T. H. Mo 《Journal of Optimization Theory and Applications》2017,173(2):357-390
The main purpose of this paper consists of providing characterizations of the inclusion of the solution set of a given conic system posed in a real locally convex topological space into a variety of subsets of the same space defined by means of vector-valued functions. These Farkas-type results are used to derive characterizations of the weak solutions of vector optimization problems (including multiobjective and scalar ones), vector variational inequalities, and vector equilibrium problems. 相似文献
14.
Michael Greenblatt 《Journal of Geometric Analysis》2018,28(2):787-816
In this paper, estimates are proven for convolution kernels associated to multipliers from a reasonably general class of compactly supported two-dimensional functions constructed out of real analytic functions. These estimates are both for overall decay rate and decay rate in specific directions. The estimates are sharp for a certain range of exponents appearing in the theorems. 相似文献
15.
《Optimization》2012,61(2):145-152
The aim of the article is to characterize the locally Lipschitz vector-valued functions which are K -quasiconvex with respect to a closed convex cone K in the sense that the sublevel sets are convex. Our criteria are written in terms of a K -quasimonotonicity notion of the generalized directional derivative and of Clarke's generalized Jacobian. This work could be compared to Sach's one in which the author gives necessary and sufficient conditions for a locally Lipschitz map f between two Euclidean spaces to be scalarly K -quasiconvex in the sense that, for any continuous linear form of the nonnegative polar cone K + , the composite function f is quasiconvex. 相似文献
16.
17.
Let T be a completely regular space and X a strictly convexn-dimensional real space. We prove that every continuous functionfrom T into the closed unit ball of X can be expressed as anaverage of eight continuous functions from T into the sphereof X if and only if dim (T) n1, where dim(T) denotesthe covering dimension of T. The proof we give can be used toprove the same fact, without hypotheses on T, when X is infinite-dimensional,although in this case it has been proved recently that a betterresult can be obtained. 相似文献
18.
19.
Michael Cwikel 《Mathematische Nachrichten》1987,132(1):153-161
A generalization of a theorem of Bergh concerning complex interpolation of nonlinear operators is applied to prove Lebedev-Milin type estimates for Taylor coefficients of composed analytic functions. 相似文献
20.
Uniqueness of the Topology on Spaces of Vector-Valued Functions 总被引:1,自引:0,他引:1
Let be a topological space without isolated points, let E bea topological linear space which is continuously embedded intoa product of countably boundedly generated topological linearspaces, and let X be a linear subspace of C(, E). If a C()is not constant on any open subset of and aX X, then it isshown that there is at most one F-space topology on X that makesthe multiplication by a continuous. Furthermore, if U is a subsetof C() which separates strongly the points of and UX X, thenit is proved that there is at most one F-space topology on Xthat makes the multiplication by a continuous for each a U. These results are applied to the study of the uniqueness ofthe F-space topology and the continuity of translation invariantoperators on the Banach space L1(G, E) for a noncompact locallycompact group G and a Banach space E. Furthermore, the problemsof the uniqueness of the F-algebra topology and the continuityof epimorphisms and derivations on F-algebras and some algebrasof vector-valued functions are considered. 相似文献