共查询到20条相似文献，搜索用时 15 毫秒
1.
Let () be the set of all continuous functions on which have a derivative ( , respectively) at least at one point . B. R. Hunt (1994) proved that is Haar null (in Christensen's sense) in .
In the present article it is proved that neither nor its complement is Haar null in . Moreover, the same assertion holds if we consider the approximate derivative (or the ``strong' preponderant derivative) instead of the ordinary derivative; these results are proved using a new result on typical (in the sense of category) continuous functions, which is of interest in its own right.
2.
In this paper we provide a general method to prove that certain nonlinear families of continuous functions contain dense linear manifolds. An application is furnished.
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It is shown that for every closed, convex and nowhere dense subset of a superreflexive Banach space there exists a Radon probability measure on so that for all . In particular, closed, convex, nowhere dense sets in separable superreflexive Banach spaces are Haar null. This is unlike the situation in separable nonreflexive Banach spaces, where there always exists a closed convex nowhere dense set which is not Haar null.
4.
P. Cannarsa P. Cardaliaguet E. Giorgieri 《Transactions of the American Mathematical Society》2007,359(6):2741-2775
Given a bounded domain in with smooth boundary, the cut locus is the closure of the set of nondifferentiability points of the distance from the boundary of . The normal distance to the cut locus, , is the map which measures the length of the line segment joining to the cut locus along the normal direction , whenever . Recent results show that this map, restricted to boundary points, is Lipschitz continuous, as long as the boundary of is of class . Our main result is the global Hölder regularity of in the case of a domain with analytic boundary. We will also show that the regularity obtained is optimal, as soon as the set of the so-called regular conjugate points is nonempty. In all the other cases, Lipschitz continuity can be extended to the whole domain . The above regularity result for is also applied to derive the Hölder continuity of the solution of a system of partial differential equations that arises in granular matter theory and optimal mass transfer.
5.
A. L. Kuz’mina 《Russian Mathematics (Iz VUZ)》2008,52(7):8-14
We study Besicovitch-type spaces of generalized almost periodic functions. The main result is a theorem on representation of linear continuous functionals that is similar to the classical result of F. Riesz. 相似文献
6.
Y. A. Fiagbedzi 《International Journal of Mathematical Education in Science & Technology》2013,44(4):617-629
The coordinates of an n-dimensional regular simplex are found. These coordinates are used to derive properties of the regular simplex that generalize their two- and three-dimensional counterparts. 相似文献
7.
We prove that a locally finite dimensional shift-invariant linear space of distributions must be a linear subspace of some shift-invariant space generated by finitely many compactly supported distributions. If the locally finite dimensional shift-invariant space is a subspace of the Hölder continuous space or the fractional Sobolev space , then the superspace can be chosen to be or , respectively.
8.
Krzysztof Ciesielski Janusz Pawlikowski 《Proceedings of the American Mathematical Society》2002,130(7):2007-2013
We show that the property
- (P)
- for every Darboux function there exists a continuous nowhere constant function such that is Darboux
- (A)
- for every subset of of cardinality there exists a uniformly continuous function such that ,
- (B)
- for an arbitrary function whose image contains a non-trivial interval there exists an of cardinality such that the restriction of to is uniformly continuous,
9.
Shunsuke Shiraishi 《Mathematical Programming》1993,58(1-3):257-262
For a real-valued convex functionf, the existence of the second-order Dini derivative assures that of the limit of the approximate second-order directional derivativef
(x
0;d, d) when 0+ and both values are the same. The aim of the present work is to show the converse of this result. It will be shown that upper and lower limits of the approximate second-order directional derivative are equal to the second-order upper and lower Dini derivatives, respectively. Consequently the existence of the limit of the approximate second-order directional derivative and that of second-order Dini derivative are equivalent.Dedicated to Professor N. Furukawa of Kyushu University for his 60th birthday. 相似文献
10.
In this study, based on a new quantum integral identity, we establish some quantum estimates of Hermite-Hadamard type inequalities for convex functions. These results generalize and improve some known results given in literatures. 相似文献
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Thomas M. Lewis 《Journal of Mathematical Analysis and Applications》2009,353(1):224-231
Katsuura's example of a continuous nowhere differentiable function is based on a fixed-point method. In this paper we use probability theory to study the increments of Katsuura's function. 相似文献
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In this paper we establish sharp H ¨older estimates of harmonic functions on a class of connected post critically finite (p.c.f.) self-similar sets, and show that functions in the domain of Laplacian ... 相似文献
17.
T. H. Sweetser III 《Journal of Optimization Theory and Applications》1977,23(4):549-562
A set-valued derivative for a function at a point is a set of linear transformations whichapproximates the function near the point. This is stated precisely, and it is shown that, in general, there is not a unique minimal set-valued derivative for functions in the family of closed convex sets of linear transformations. For Lipschitz functions, a construction is given for a specific set-valued derivative, which reduces to the usual derivative when the function is strongly differentiable, and which is shown to be the unique minimal set-valued derivative within a certain subfamily of the family of closed convex sets of linear transformations. It is shown that this constructed set may be larger than Clarke's and Pourciau's set-valued derivatives, but that no irregularity is introduced.The author would like to thank Professor H. Halkin for numerous discussions of the material contained here. 相似文献
18.
Ph. Clé ment G. Gripenberg S-O. Londen 《Transactions of the American Mathematical Society》2000,352(5):2239-2260
The equation where and are fractional derivatives of order and is studied. It is shown that if , , and are Hölder-continuous and , then there is a solution such that and are Hölder-continuous as well. This is proved by first considering an abstract fractional evolution equation and then applying the results obtained to (). Finally the solution of () with is studied. 相似文献
19.
Let hR denote an L∞ normalized Haar function adapted to a dyadic rectangle R⊂d[0,1]. We show that for choices of coefficients α(R), we have the following lower bound on the L∞ norms of the sums of such functions, where the sum is over rectangles of a fixed volume:
20.
Yasuhiro Gotoh 《Proceedings of the American Mathematical Society》1999,127(5):1443-1451
Let denote the space of all positive superharmonic functions on a domain . Lindqvist showed that is a bounded subset of . Using this, we give a characterization of finitely connected -dimensional uniform domains and remarks on Hölder domains.