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121.
A multiresolution analysis is defined in a class of locally compact abelian groups G. It is shown that the spaces of integrable functions
and the complex Radon measures M(G) admit a simple characterization in terms of this multiresolution analysis. 相似文献
122.
Marian Nowak 《Proceedings of the American Mathematical Society》2001,129(10):2947-2953
Let be an ideal of over a -finite measure space and let be the Köthe dual of with . Let be a real Banach space, and the topological dual of . Let be a subspace of the space of equivalence classes of strongly measurable functions and consisting of all those for which the scalar function belongs to . For a subset of for which the set is -bounded the following statement is equivalent to conditional -compactness: the set is conditionally -compact and is a conditionally weakly compact subset of for each , with . Applications to Orlicz-Bochner spaces are given.
123.
We study (set-valued) mappings of bounded -variation defined on the compact interval I and taking values in metric or normed linear spaces X. We prove a new structural theorem for these mappings and extend Medvedev's criterion from real valued functions onto mappings with values in a reflexive Banach space, which permits us to establish an explicit integral formula for the -variation of a metric space valued mapping. We show that the linear span GV
(I;X) of the set of all mappings of bounded -variation is automatically a Banach algebra provided X is a Banach algebra. If h:I× X Y is a given mapping and the composition operator is defined by (f)(t)=h(t,f(t)), where tI and f:I X, we show that :GV
(I;X) GV
(I;Y) is Lipschitzian if and only if h(t,x)=h0(t)+h1(t)x, tI, xX. This result is further extended to multivalued composition operators with values compact convex sets. We prove that any (not necessarily convex valued) multifunction of bounded -variation with respect to the Hausdorff metric, whose graph is compact, admits regular selections of bounded -variation. 相似文献
124.
We improve on a recent result of Saradha giving a transcendence measure for the quotient
of a period of an elliptic curve defined over by its associated quasi-period. In an (almost successful) attempt to include in a single measure both this result and that obtained by Reyssat in 1980, we blend into the modular method ideas related to modular but also hypergeometric functions, as appearing e.g. in André's work, as well as some Galois considerations. 相似文献
125.
The problem of estimating of the law
(in the space
of the paths) and the common marginal distribution for a strictly stationary ergodic process X is discussed. We show, in particular, that:(1) The empirical measure
with probability 1 converges weakly in
to
.(2) The empirical measure
corresponding to the path
, converges a.s. when T in total variation to the marginal law if and only if the local time for X exists. (3) The L
p-convergence of the empirical densities f
T to the marginal one is studied.(4) A version of the CLT for empirical densities f
T provided both the mixing properties and the local time of the underlying process are good enough is given. 相似文献
126.
Marian Nowak 《Czechoslovak Mathematical Journal》2000,50(2):401-414
Let
be a real Banach space and let E be an ideal of L
0 over a -finite measure space (, , ). Let (X) be the space of all strongly -measurable functions f: X such that the scalar function
, defined by
, belongs to E. The paper deals with strong topologies on E(X). In particular, the strong topology
the order continuous dual of E(X)) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies. 相似文献
127.
L. Rodrí guez-Piazza M. C. Romero-Moreno 《Transactions of the American Mathematical Society》2000,352(1):379-395
Let be a real number such that and its conjugate exponent . We prove that for an operator defined on with values in a Banach space, the image of the unit ball determines whether belongs to any operator ideal and its operator ideal norm. We also show that this result fails to be true in the remaining cases of . Finally we prove that when the result holds in finite dimension, the map which associates to the image of the unit ball the operator ideal norm is continuous with respect to the Hausdorff metric.
128.
Cristian E. Gutié rrez Qingbo Huang 《Transactions of the American Mathematical Society》2000,352(9):4381-4396
In this paper we establish several geometric properties of the cross sections of generalized solutions to the Monge-Ampère equation , when the measure satisfies a doubling property. A main result is a characterization of the doubling measures in terms of a geometric property of the cross sections of . This is used to obtain estimates of the shape and invariance properties of the cross sections that are valid under appropriate normalizations.
129.
On the Distribution of Long-Term Time Averages on Symbolic Space 总被引:2,自引:0,他引:2
The pressure was studied in a rather abstract theory as an important notion of the thermodynamic formalism. The present paper gives a more concrete account in the case of symbolic spaces, including subshifts of finite type. We relate the pressure of an interaction function to its long-term time averages through the Hausdorff and packing dimensions of the subsets on which has prescribed long-term time-average values. Functions with values in
d
are considered. For those depending only on finitely many symbols, we get complete results, unifying and completing many partial results. 相似文献
130.
In this contribution we discuss the role disordered (or random) systems have played in the study of non-Gibbsian measures.
This role has two main aspects, the distinction between which has not always been fully clear: 1) From disordered systems: Disordered systems can be used as a tool; analogies with, as well as results and methods from the study
of random systems can be employed to investigate non-Gibbsian properties of a variety of measures of physical and mathematical
interest. 2) Of disordered systems: Non-Gibbsianness is a property of various (joint) measures describing quenched disordered systems. We
discuss and review this distinction and a number of results related to these issues. Moreover, we discuss the mean-field version
of the non-Gibbsian property, and present some ideas how a Kac limit approach might connect the finite-range and the mean-field
non-Gibbsian properties. 相似文献