共查询到20条相似文献,搜索用时 15 毫秒
1.
Hiroaki Aikawa Tero Kilpeläinen Nageswari Shanmugalingam Xiao Zhong 《Potential Analysis》2007,26(3):281-301
We establish a scale-invariant version of the boundary Harnack principle for p-harmonic functions in Euclidean C
1,1-domains and obtain estimates for the decay rates of positive p-harmonic functions vanishing on a segment of the boundary in terms of the distance to the boundary. We use these estimates
to study the behavior of conformal Martin kernel functions and positive p-superharmonic functions near the boundary of the domain.
H. A. was partially supported by Grant-in-Aid for (B) (2) (No. 15340046) Japan Society for the Promotion of Science. N. S.
was partially supported by NSF grant DMS-0355027. X. Z. was partially supported by the Taft foundation. 相似文献
2.
Akhlad Iqbal Shahid Ali I. Ahmad 《Journal of Optimization Theory and Applications》2012,155(1):239-251
In this paper, we introduce a new class of sets and a new class of functions called geodesic E-convex sets and geodesic E-convex functions on a Riemannian manifold. The concept of E-quasiconvex functions on R n is extended to geodesic E-quasiconvex functions on Riemannian manifold and some of its properties are investigated. Afterwards, we generalize the notion of epigraph called E-epigraph and discuss a characterization of geodesic E-convex functions in terms of its E-epigraph. Some properties of geodesic E-convex sets are also studied. 相似文献
3.
M. A. Tawhid 《Computational Optimization and Applications》2008,39(1):51-74
This paper deals with nonnegative nonsmooth generalized complementarity problem, denoted by GCP(f,g). Starting with H-differentiable functions f and g, we describe H-differentials of some GCP functions and their merit functions. We show how, under appropriate conditions on H-differentials of f and g, minimizing a merit function corresponding to f and g leads to a solution of the generalized complementarity problem. Moreover, we generalize the concepts of monotonicity, P
0-property and their variants for functions and use them to establish some conditions to get a solution for generalized complementarity
problem. Our results are generalizations of such results for nonlinear complementarity problem when the underlying functions
are C
1, semismooth, and locally Lipschitzian. 相似文献
4.
In the univariate case there are certain equivalences between the
nonlinear approximation methods that use piecewise polynomials and
those that use rational functions. It is known that for certain
parameters the respective approximation spaces are identical and
may be described as Besov spaces. The characterization of the
approximation spaces of the multivariate nonlinear approximation
by piecewise polynomials and by rational functions is not known.
In this work we compare between the two methods in the bivariate
case. We show some relations between the approximation spaces of
piecewise polynomials defined on n triangles and those of
bivariate rational functions of total degree n which are
described by n parameters. Thus we compare two classes of
approximants with the same number Cn of parameters. We consider
this the proper comparison between the two methods. 相似文献
5.
We study the relation between different spaces of vector-valued polynomials and analytic functions over dual-isomorphic Banach
spaces. Under conditions of regularity onE andF, we show that the spaces ofX-valuedn-homogeneous polynomials and analytic functions of bounded type onE andF are isomorphic wheneverX is a dual space. Also, we prove that many of the usual subspaces of polynomials and analytic functions onE andF are isomorphic without conditions on the involved spaces. 相似文献
6.
David Kronus 《Annals of Operations Research》2011,188(1):263-278
Every k-interval Boolean function f can be represented by at most k intervals of integers such that vector x is a truepoint of f if and only if the integer represented by x belongs to one of these k (disjoint) intervals. Since the correspondence of Boolean vectors and integers depends on the order of bits an interval representation
is also specified with respect to an order of variables of the represented function. Interval representation can be useful
as an efficient representation for special classes of Boolean functions which can be represented by a small number of intervals.
In this paper we study inclusion relations between the classes of threshold and k-interval Boolean functions. We show that positive 2-interval functions constitute a (proper) subclass of positive threshold
functions and that such inclusion does not hold for any k>2. We also prove that threshold functions do not constitute a subclass of k-interval functions, for any k. 相似文献
7.
By an ℱK-convex function on a length metric space, we mean one that satisfies f
n
≥ −Kf on all unitspeed geodesics. We show that natural ℱK-convex (-concave) functions occur in abundance on metric spaces of curvature bounded above (below) by K in the sense of Alexandrov. We prove Lipschitz extension and approximation theorems for ℱK-convex functions on CAT(K) spaces.
Received: 10 May 2002
Mathematics Subject Classification (2000): 53C70, 52A41 相似文献
8.
P. Oswald 《Journal of Mathematical Sciences》2008,155(1):109-128
In [9], we proved numerically that spaces generated by linear combinations of some two-dimensional Haar functions exhibit
unexpectedly nice orders of approximation for solutions of the single-layer potential equation in a rectangle. This phenomenon
is closely related, on the one hand, to the properties of the approximation method of hyperbolic crosses and on the other
to the existence of a strong singularity for solutions of such boundary integral equations. In the present paper, we establish
several results on the approximation for the hyperbolic crosses and on the best N-term approximations by linear combinations of Haar functions in the H
s
-norms, −1 < s < 1/2; this provides a theoretical base for our numerical research. To the author's best knowledge, the negative smoothness
case s < 0 was not studied earlier.
__________
Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 25, Theory of Functions, 2007. 相似文献
9.
A. A. Koshelev 《Russian Mathematics (Iz VUZ)》2011,55(6):53-63
We obtain close two-sided estimates for the best approximation of Laplace operator by linear bounded operators on the class
of functions for which the square of the Laplace operator belongs to the L
p
-space. We estimate the best constant in the corresponding Kolmogorov inequality and the error of the optimal recovery of
values of the Laplace operator on functions from this class defined with an error. In a particular case (p = 2) we solve all three problems exactly. 相似文献
10.
V. I. Buslaev 《Ukrainian Mathematical Journal》2010,62(3):358-372
We obtain explicit formulas that express the Hankel determinants of functions given by their expansions in continued P-fractions in terms of the parameters of the fraction. As a corollary, we obtain a lower bound for the capacity of the set
of singular points of these functions, an analog of the van Vleck theorem for P-fractions with limit-periodic coefficients, another proof of the Gonchar theorem on the Leighton conjecture, and an upper
bound for the radius of the disk of meromorphy of a function given by a C-fraction. 相似文献
11.
We study extension of operators T: E→ L0([0, 1]), where E is an F–function space and L0([0, 1]) the space of measurable functions with the topology of convergence in measure, to domains larger than E, and we study the properties of such domains. The main tool is the integration of scalar functions with respect to stochastic
measures and the corresponding spaces of integrable functions.
Partially supported by D.G.I. #MTM2006-13000-C03-01 (Spain). 相似文献
12.
Wolfram Bauer 《Mathematische Nachrichten》2008,281(6):764-785
Let E be a 𝒟ℱ𝒩‐space and let U ⊂ E be open. By applying the nuclearity of the Fréchet space ℋ︁(U) of holomorphic functions on U we show that there are finite measures μ on U leading to Bergman spaces of μ ‐square integrable holomorphic functions. We give an explicit construction for μ by using infinite dimensional Gaussian measures. Moreover, we prove boundary estimates for the corresponding Bergman kernels Kμ on the diagonal and we give an application of our results to liftings of μ ‐square integrable Banach space valued holomorphic functions over U. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
In this paper, we describe the H-differentials of some well known NCP functions and their merit functions. We show how, under appropriate conditions on an
H-differential of f, minimizing a merit function corresponding to f leads to a solution of the nonlinear complementarity problem. Our results give a unified treatment of such results for C
1-functions, semismooth-functions, and locally Lipschitzian functions. Illustrations are given to show the usefulness of our
results. We present also a result on the global convergence of a derivative-free descent algorithm for solving the nonlinear
complementarity problem.
The first author is deeply indebted to Professor M. Seetharama Gowda for his numerous helpful suggestions and encouragement.
Special thanks to Professor J.-P. Crouzeix and an anonymous referees for their constructive suggestions which led to numerous
improvements in the paper. The research of the first author was supported in part by the Natural Sciences and Engineering
Research Council of Canada and Scholar Activity Grant of Thompson Rivers University. The research of the second author was
supported by the Natural Sciences and Engineering Research Council of Canada. 相似文献
14.
We consider the problem of characterization of subspaces of uniqueness of an element of the best nonsymmetric L
1-approximation of functions that are continuous on a metric compact set of functions with values in a KB-space. We find classes of test functions that characterize the uniqueness of an element of the best nonsymmetric approximation.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 867–878, July, 2008. 相似文献
15.
We investigate exact constants in Jackson-type inequalities in the space L
2 for the approximation of functions on an axis by the subspace of entire functions of exponential type.
A. A. Ligun (Deceased.)
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 1, pp. 92–98, January, 2009. 相似文献
16.
N. V. Parfinovych 《Ukrainian Mathematical Journal》2005,57(10):1652-1662
We determine the exact order of relative widths of classes W
1
r
of periodic functions in the space L
1 as n → ∞ under restrictions on higher derivatives of approximating functions.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1409–1417, October, 2005. 相似文献
17.
Wolter Groenevelt 《Constructive Approximation》2009,29(1):85-127
Big q-Jacobi functions are eigenfunctions of a second-order q-difference operator L. We study L as an unbounded self-adjoint operator on an L
2-space of functions on ℝ with a discrete measure. We describe explicitly the spectral decomposition of L using an integral transform ℱ with two different big q-Jacobi functions as a kernel, and we construct the inverse of ℱ.
相似文献
18.
A novel way of generating higher-order iteration functions for the computation of pth roots of complex numbers is the main contribution of the present work. The behavior of some of these iteration functions
will be analyzed and the conditions on the starting values that guarantee the convergence will be stated. The illustration
of the basins of attractions of the pth roots will be carried out by some computer generated plots. In order to compare the performance of the iterations some
numerical examples will be considered. 相似文献
19.
20.
Renata Wiertelak 《Periodica Mathematica Hungarica》2011,63(1):71-79
A generalization of density point with respect to category and I(J)-density topology has been presented in [5]. This papers deals with some basic properties of the corresponding I(J)-approximately continuous functions and gives answer when these functions are of the first Baire class and when they are
Darboux functions. 相似文献