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81.
In this paper, we present some alternative definitions of Besov spaces of generalized smoothness, defined via Littlewood–Paley‐type decomposition, involving weak derivatives, polynomials, convolutions and generalized interpolation spaces. 相似文献
82.
U. Luther 《Annali di Matematica Pura ed Applicata》2003,182(2):161-200
We show that the representation theorem for classical approximation spaces can be generalized to spaces A(X,l
q
(ℬ))={f∈X:{E
n
(f)}∈l
q
(ℬ)} in which the weighted l
q
-space l
q
(ℬ) can be (more or less) arbitrary. We use this theorem to show that generalized approximation spaces can be viewed as real
interpolation spaces (defined with K-functionals or main-part K-functionals) between couples of quasi-normed spaces which satisfy certain Jackson and Bernstein-type inequalities. Especially,
interpolation between an approximation space and the underlying quasi-normed space leads again to an approximation space.
Together with a general reiteration theorem, which we also prove in the present paper, we obtain formulas for interpolation
of two generalized approximation spaces.
Received: December 6, 2001; in final form: April 2, 2002?Published online: March 14, 2003 相似文献
83.
We prove that the weighted error of approximation by the Szász-Mirakyan-type operator introduced in [1] is equivalent to the
modulus of smoothness of the function. This result is analogous to previous results for Bernstein-type operators obtained
by Ditzian-Ivanov and Szabados.
Research supported by Hungarian Scientific Research Fund (OTKA), Grant No. T-049196. 相似文献
84.
We prove that for Hilbert space operators and , it follows that
where . Using the concept of -Gateaux derivative, we apply this result to characterize orthogonality in the sense of James in , and to give an easy proof of the characterization of smooth points in .
,\end{displaymath}">
where . Using the concept of -Gateaux derivative, we apply this result to characterize orthogonality in the sense of James in , and to give an easy proof of the characterization of smooth points in .
85.
宣培才 《宁波大学学报(理工版)》1993,(2)
借助于一类K—泛函和加权光滑模之间的等价关系,给出了积分型Meyer-Konig和Zeller算子在一致逼近意义的特征刻划. 相似文献
86.
A.J. Guirao P. Hájek V. Montesinos 《Journal of Mathematical Analysis and Applications》2010,367(1):29-33
We show a unified method of proving the existence of C1-Fréchet smooth and Lipschitz mappings which are surjective or whose range of the derivative contains the whole dual unit ball. As an application, under Martin's Maximum axiom, we obtain a complete result for those spaces with density character ω1. 相似文献
87.
Hsien-Chung Wu 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):469-477
The conventional Hahn-Banach extension theorem based on vector space has been widely used to obtain many important and interesting results in nonlinear analysis, vector optimization and mathematical economics. Although the interval space is not a real vector space, the Hahn-Banach extension theorems based on interval spaces and nonstandard normed interval spaces can still be derived in this paper, which also shows the possible applications by considering the interval-valued problems in nonlinear analysis, vector optimization and mathematical economics. 相似文献
88.
89.
A new third‐order WENO scheme is proposed to achieve the desired order of convergence at the critical points for scalar hyperbolic equations. A new reference smoothness indicator is introduced, which satisfies the sufficient condition on the weights for the third‐order convergence. Following the truncation error analysis, we have shown that the proposed scheme achieves the desired order accurate for smooth solutions with arbitrary number of vanishing derivatives if the parameter ε satisfies certain conditions. We have made a comparative study of the proposed scheme with the existing schemes such as WENO‐JS, WENO‐Z, and WENO‐N3 through different numerical examples. The result shows that the proposed scheme (WENO‐MN3) achieves better performance than these schemes. 相似文献
90.
We polish a theorem and its proof of Daubechies by removing the boundedness condition. The importance of the original theorem is that it links the vanishing of moments to the smoothness. 相似文献