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991.
Let: E M be a fiber bundle and let be an infinitesimal Lie transformation group acting onE. We announce various new results concerning the cohomology of the invariant variational bicomplex (
*,*
(J(E)), dH, dV) and the associated invariant Euler-Lagrange complex. As one application of our general theory, we completely solve the local invariant inverse problem of the calculus of variations for finite-dimensional infinitesimal Lie transformation groups. 相似文献
992.
A classic 1970 paper of B. Muckenhoupt established necessary and sufficient conditions for weightedL
p
convergence of Hermite series, that is, orthogonal expansions corresponding to the Hermite weight. We generalize these to orthogonal expansions for a class of Freud weightsW
2:=e
–2Q
, by first proving a bound for the difference of the orthonormal polynomials of degreen+1 andn–1 of the weightW
2. Our identical necessary and sufficient conditions close a slight gap in Muckenhoupt's conditions for the Hermite weight at least forp>1. Moreover, our necessary conditions apply whenQ(x)=|x|, >1 while our sufficient conditions apply at least for =2,4,6,....Communicated by Vilmos Totik. 相似文献
993.
V. G. Kravchenko A. B. Lebre G. S. Litvinchuk F. S. Teixeira 《Integral Equations and Operator Theory》1995,21(3):342-354
The solution to a normalization problem for singular integral operators with Carleman shift and degenerate and unbounded coefficients inL
p
() is obtained, where is either the unit circle or the real line. The approach followed consists mainly in two steps: the reduction to a singular integral operator with bounded coefficients and the use of the solution to an abstract normalization problem.This research was supported by JNICT under the grant PBIC/C/CEN/1040/92. 相似文献
994.
Chuu-Lian Terng 《Journal of Geometric Analysis》1995,5(1):129-150
An isometricH-action on a Riemannian manifoldX is calledpolar if there exists a closed submanifoldS ofX that meets everyH-orbit and always meets orbits orthogonally (S is called a section). LetG be a compact Lie group equipped with a biinvariant metric,H a closed subgroup ofG ×G, and letH act onG isometrically by (h
1,h
2) ·x = h
1
xh
2
−1
· LetP(G, H) denote the group ofH
1-pathsg: [0, 1] →G such that (g(0),g (1)) ∈H, and letP(G, H) act on the Hilbert spaceV = H
0([0, 1], g) isometrically byg * u = gug
−1 −g′g
−1. We prove that if the action ofH onG is polar with a flat section then the action ofP(G, H) onV is polar. Principal orbits of polar actions onV are isoparametric submanifolds ofV and are infinite-dimensional generalized real or complex flag manifolds. We also note that the adjoint actions of affine
Kac-Moody groups and the isotropy action corresponding to an involution of an affine Kac-Moody group are special examples
ofP(G, H)-actions for suitable choice ofH andG.
Work supported partially by NSF Grant DMS 8903237 and by The Max-Planck-Institut für Mathematik in Bonn. 相似文献
995.
We describe sufficient conditions for transferring from locally compact abelian groups to measure spaces the weak-type bounds
of maximal operators defined by multipliers of weak type. This leads to homomorphism theorems for maximal multiplier operators.
Communicated by Guido Weiss 相似文献
996.
Philippe Choné 《Potential Analysis》1995,4(3):269-296
Let be an open set inR
2 andI be a conformally invariant functional defined onH
1(,R
d
). Letu be a critical point ofI. We show that, ifu is apriori assumed to be bounded, thenu is smooth in , up to (ifu
|
is smooth). This is a partial (positive) answer to a conjecture of S. Hildebrandt [13]. As an application, we establish a regularity result for weak solutions to the equation of surfaces of prescribed mean curvature in a three-dimensional compact riemannian manifold. 相似文献
997.
Summary The concept of hull convexity (midpoint hull convexity) for set-valued functions in vector spaces is examined. This concept, introduced by A. V. Fiacco and J. Kyparisis (Journal of Optimization Theory and Applications,43 (1986), 95–126), is weaker than one of convexity (midpoint convexity).The main result is a sufficient condition for a midpoint hull convex set-valued function to be continuous. This theorem improves a result obtained by K. Nikodem (Bulletin of the Polish Academy of Sciences, Mathematics,34 (1986), 393–399). 相似文献
998.
Francis Choucroun 《Geometriae Dedicata》1994,53(1):69-74
Résumé On décrit une bijection canonique qui associe à un bon espace ultramétrique, localement compact, non compact, un arbre pointé par un bout: cet espace s'identifie à l'ensemble des autres bouts.
We describe a canonical bijection, which associates a tree with a chosen end to a nice ultrametric, locally compact, non-compact space: this space is identified with the set of other ends.相似文献
999.
Eike Hertel 《Geometriae Dedicata》1994,52(3):215-220
A subsetS of a metric space (X,d) is calledd-convex if for any pair of pointsx,y S each pointz X withd(x,z) +d(z,y) =d(x,y) belongs toS. We give some results and open questions concerning isometric and convexity-preserving embeddings of finite metric spaces into standard spaces and the number ofd-convex sets of a finite metric space. 相似文献
1000.
There is a new method of constructing generalized quadrangles (GQs) given by S. Löwe, which is based on covering of nets; all GQs with a regular point can be represented in this way. Here we give a method of constructing GQs with a regular point using the so-called content functions on nets. In the last part of the paper we lay the foundations for a research project aiming to use the more general notion of content to classify GQs and maybe to construct new ones.Both authors acknowledge the financial support by CRUI and DAAD in the frame of Programma Vigoni, which made this work possible. 相似文献