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91.
Gregory L. Eyink 《Journal of statistical physics》1995,78(1-2):353-375
Parisi and Frisch proposed some time ago an explanation for multiscaling of turbulent velocity structure functions in terms of a multifractal hypothesis, i.e., they conjecture that the velocity field has local Hölder exponents in a range [h
min,h
max], with exponents <h occurring on a setS(h) with a fractal dimensionD(h). Heuristic reasoning led them to an expression for the scaling exponentz
p
ofpth order as the Legendre transform of the codimensiond-D(h). We show here that a part of the multifractal hypothesis is correct under even weaker assumptions: namely, if the velocity field hasL
p
-mean Hölder indexs, i.e., if it lies in the Besov spaceB
p
s,
, then local Hölder regularity is satisfied. Ifs<d/p, then the hypothesis is true in a generalized sense of Hölder space with negative exponents and we discuss the proper definition of local Hölder classes of negative index. Finally, if a certain box-counting dimension exists, then the Legendre transform of its codimension gives the scaling exponentz
p
, and, more generally, the maximal Besov index of order,p, ass
p
=z
p
/p. Our method of proof is derived from a recent paper of S. Jaffard using compactly-supported, orthonormal wavelet bases and gives an extension of his results. We discuss implications of the theorems for ensemble-average scaling and fluid turbulence. 相似文献
92.
Vladimir Dobrić 《Journal of Theoretical Probability》1994,7(1):129-134
IfB is a weakly compactly generated Banach space andf: (S,S, ) satisfies the strong law of large numbers, thenf=f
1+f
2, wheref
1 is Bochner -integrable andf
2 is Pettis -integrable with Pettis norm 0. The decomposition is unique. 相似文献
93.
We prove the Cramér theorem forK-invariant Gaussian measures on irreducible symmetric spacesX=G/K withG semisimple noncompact. To do this we use a kind of Abel transform ofK-invariant measures onX.This research is supported by KBN Grant. 相似文献
94.
Alexander Koldobsky 《Journal of Theoretical Probability》1994,7(1):135-145
Let μ be a measure in a Banach spaceE, f be an even function onR. We consider the potentialg(a)=f E f(‖x?a‖)dμ(x). The question is as follows: For whichf does the potentialg determine μ uniquely? In this article we give answers in the cases whereE=l ∞ n and wheref(t)=|t| p andE is a finite dimensional Banach space with symmetric analytic norm. Calculating the Fourier transform of the functionf(‖x‖ ∞) we give a new proof of the J. Misiewicz's result that the functionf(‖x‖ ∞) is positive definite only iff is a constant function. 相似文献
95.
Let and be real Banach spaces. A map between and is called an -bi-Lipschitz map if for all . In this note we show that if is an -bi-Lipschitz map with from onto , then is almost linear. We also show that if is a surjective -bi-Lipschitz map with , then there exists a linear isomorphism such that
where as and .
96.
Friedbert Prü fer Franco Tricerri Lieven Vanhecke 《Transactions of the American Mathematical Society》1996,348(11):4643-4652
We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.
97.
Eva Matousková Charles Stegall 《Proceedings of the American Mathematical Society》1996,124(4):1083-1090
A Banach space is not reflexive if and only if there exist a closed separable subspace of and a convex closed subset of with empty interior which contains translates of all compact sets in . If, moreover, is separable, then it is possible to put .
98.
V. I. Chilin P. G. Dodds A. A. Sedaev F. A. Sukochev 《Transactions of the American Mathematical Society》1996,348(12):4895-4918
We present several characterizations of Kadec-Klee properties in symmetric function spaces on the half-line, based on the -functional of J. Peetre. In addition to the usual Kadec-Klee property, we study those symmetric spaces for which sequential convergence in measure (respectively, local convergence in measure) on the unit sphere coincides with norm convergence.
99.
Jun-ichi Tanaka 《Transactions of the American Mathematical Society》1996,348(10):4113-4129
Using the Stone-\v{C}ech compactification of integers, we introduce a free extension of an almost periodic flow. Together with some properties of outer functions, we see that, in a certain class of ergodic Hardy spaces , , the corresponding subspaces are all singly generated. This shows the existence of maximal weak- Dirichlet algebras, different from of the disc, for which the single generator problem is settled.
100.
Bolis Basit Hans Gü nzler 《Transactions of the American Mathematical Society》1996,348(11):4489-4500
Let be a semigroup and a topological space. Let be an Abelian topological group. The right differences of a function are defined by for . Let be continuous at the identity of for all in a neighbourhood of . We give conditions on or range under which is continuous for any topological space . We also seek conditions on under which we conclude that is continuous at for arbitrary . This led us to introduce new classes of semigroups containing all complete metric and locally countably compact quasitopological groups. In this paper we study these classes and explore their relation with Namioka spaces.