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991.
We consider best -term approximation in with wave packets generated by a single refinable function. The main examples of wave packets are orthonormal wavelets, or more generally wavelet frames based on a multiresolution analysis (so-called framelets). The approximation classes associated with best -term approximation in for a large class of wave packets are completely characterized in terms of Besov spaces.
As an application of the main result, we show that for -term approximation in with elements from an oversampled version of a framelet system with compactly supported generators, the associated approximation classes turn out to be (essentially) Besov spaces.
992.
Elias Katsoulis David W. Kribs 《Transactions of the American Mathematical Society》2005,357(9):3739-3755
Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid algebras, and show that joint similarity implies joint unitary equivalence for such families. For each graph we prove a generalization of von Neumann's inequality which applies to row contractions of operators on Hilbert space which are related to the graph in a natural way. This yields a functional calculus determined by quiver algebras and free semigroupoid algebras. We establish a generalization of Coburn's theorem for the -algebra of a CKT family, and prove a universality theorem for -algebras generated by these families. In both cases, the -algebras generated by quiver algebras play the universal role.
993.
It is known that the Banach completion Y = bX of a normed lattice X need not preserve the properties to be Dedekind complete or σ-Dedekind complete. In this paper it is proved that the countable
interpolation property and the property to be sequentially order complete are preserved under the Banach completion. To prove
this results we found some sufficient conditions (which are close to necessary ones) on X which secure for Y to have the countable interpolation property and (respectively) to be sequentially order complete. These conditions are obtained
with the help of the newly developed techniques based on representations of normed lattices. It is well known that order continuity,
and σ-order continuity of a norm are preserved under the Banach completion. Here necessary and sufficient conditions on X to secure these properties in Y are discussed.
Mathematics Subject Classification 2000: 46B42, 46E15 相似文献
994.
Gudrun Schappacher 《Applications of Mathematics》2005,50(4):355-386
The notion of the Orlicz space is generalized to spaces of Banach-space valued functions. A well-known generalization is based on N-functions of a real variable. We consider a more general setting based on spaces generated by convex functions defined on a Banach space. We investigate structural properties of these spaces, such as the role of the delta-growth conditions, separability, the closure of
, and representations of the dual space. 相似文献
995.
L. Yu. Cherednikova 《Mathematical Notes》2005,77(5-6):715-725
Suppose that
is a system of continuous subharmonic functions in the unit disk
and
is the class of holomorphic functions f in
such that log|f(z)| ≤ B
f
p
f
(z) + C
f
, z ∈
, where B
f
and C
f
are constants and p
f
∈
. We obtain sufficient conditions for a given number sequence Λ = { λn} ⊂
to be a subsequence of zeros of some nonzero holomorphic function from
, i.e., Λ is a nonuniqueness sequence for
.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 775–787.Original Russian Text Copyright ©2005 by L. Yu. Cherednikova. 相似文献
996.
Yu. G. Safarov 《Functional Analysis and Its Applications》2005,39(4):301-307
Let ? be a convex function on ?, let ?(σ) be a pseudodifferential operator with symbol σ, let Λσ be the set of its eigenvalues, and let m(λ) be the multiplicity of an eigenvalue λ ∈ Λσ. Under certain natural assumptions about properties of pseudodifferential operators, we prove that \(\sum {_{\lambda \in \Lambda _\sigma } m(\lambda )} \varphi (\lambda ) \leqslant \operatorname{Tr} L(\varphi (\sigma )) + R\), where R is an error term of the same order as the remainder term in the Garding inequality. 相似文献
997.
In this article, mixture distributions and weighted likelihoods are derived within an information-theoretic framework and
shown to be closely related. This surprising relationship obtains in spite of the arithmetic form of the former and the geometric
form of the latter. Mixture distributions are shown to be optima that minimize the entropy loss under certain constraints.
The same framework implies the weighted likelihood when the distributions in the mixture are unknown and information from
independent samples generated by them have to be used instead. Thus the likelihood weights trade bias for precision and yield
inferential procedures such as estimates that can be more reliable than their classical counterparts. 相似文献
998.
Fu-Chuen Chang 《Annals of the Institute of Statistical Mathematics》2005,57(4):833-844
This paper is concerned with the problem of computing approximateD-optimal design for polynomial regression with analytic weight function on a interval [m
0-a,m
0+a]. It is shown that the structure of the optimal design depends ona and weight function. Moreover, the optimal support points and weights are analytic functions ofa ata=0. We make use of a Taylor expansion to provide a recursive procedure for calculating theD-optimal designs. 相似文献
999.
We consider isometric embedding of trees into the infinite graph Zm whose vertices are the m-dimensional lattice points where two vertices a=(a1,a2,…,am) and b=(b1,b2,…,bm) are adjacent if and only if |ai-bi|?1 for 1?i?m. Linial, London, and Rabinovich have shown that this can be done with , where t is the number of leaves. In this note, we sketch a proof that . 相似文献
1000.
Vlad Timofte 《Journal of Mathematical Analysis and Applications》2005,304(2):652-667
We prove that homogeneous symmetric polynomial inequalities of degree p∈{4,5} in n positive1 variables can be algorithmically tested, on a finite set depending on the given inequality (Theorem 13); the test-set can be obtained by solving a finite number of equations of degree not exceeding p−2. Section 3 discusses the structure of the ordered vector spaces and . In Section 4, positivity criteria for degrees 4 and 5 are stated and proved. The main results are Theorems 10-14. Part III of this work will be concerned with the construction of extremal homogeneous symmetric polynomials (best inequalities) of degree 4 in n positive variables. 相似文献