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1.
2.
In this paper, we introduce the notion of -decomposability of probability density functions in one dimension. Using -decomposability, we derive an inequality that applies to all symmetric unimodal densities. Our inequality involves only
the standard deviation of the densities concerned. The concept of -decomposability can be used as a non-parametric criterion for mode-finding and cluster analysis. 相似文献
3.
M. Amélia Bastos Claudio A. Fernandes Yuri I. Karlovich 《Complex Analysis and Operator Theory》2008,2(2):241-272
The C*-subalgebra of generated by all multiplication operators by slowly oscillating and piecewise continuous functions, by the Cauchy singular
integral operator and by the range of a unitary representation of an amenable group of diffeomorphisms with any nonempty set of common fixed points is studied. A symbol calculus for the C*-algebra and a Fredholm criterion for its elements are obtained. For the C*-algebra composed by all functional operators in , an invertibility criterion for its elements is also established. Both the C*-algebras and are investigated by using a generalization of the local-trajectory method for C*-algebras associated with C*-dynamical systems which is based on the notion of spectral measure.
Submitted: April 30, 2007. Accepted: November 5, 2007. 相似文献
4.
In this paper we offer a computational approach to the spectral function for a finite family of commuting operators, and give
applications. Motivated by questions in wavelets and in signal processing, we study a problem about spectral concentration
of integral translations of functions in the Hilbert space . Our approach applies more generally to families of n arbitrary commuting unitary operators in a complex Hilbert space , or equivalent the spectral theory of a unitary representation U of the rank-n lattice in . Starting with a non-zero vector , we look for relations among the vectors in the cyclic subspace in generated by ψ. Since these vectors involve infinite “linear combinations,” the problem arises of giving geometric characterizations of these non-trivial linear
relations. A special case of the problem arose initially in work of Kolmogorov under the name L
2-independence. This refers to infinite linear combinations of integral translates of a fixed function with l
2-coefficients. While we were motivated by the study of translation operators arising in wavelet and frame theory, we stress
that our present results are general; our theorems are about spectral densities for general unitary operators, and for stochastic
integrals.
Work supported in part by the U.S. National Science Foundation. 相似文献
5.
Linus Carlsson 《Mathematische Zeitschrift》2009,261(1):189-200
We show a sufficient condition for a domain in to be a H
∞-domain of holomorphy. Furthermore if a domain has the Gleason property at a point and the projection of the n − 1th order generalized Shilov boundary does not coincide with Ω then is schlicht. We also give two examples of pseudoconvex domains in which the spectrum is non-schlicht and satisfy several
other interesting properties.
相似文献
6.
Let be a saturated formation. We describe minimal non- -, minimal non- -, and minimal non-metabelian groups.
Dedicated to L. A. Shemetkov on the occasion of his seventieth birthday. 相似文献
7.
We present a new distance characterization of Aleksandrov spaces of non-positive curvature. By introducing a quasilinearization
for abstract metric spaces we draw an analogy between characterization of Aleksandrov spaces and inner product spaces; the
quasi-inner product is defined by means of the quadrilateral cosine—a metric substitute for the angular measure between two
directions at different points. Our main result states that a geodesically connected metric space is an Aleksandrov domain (also known as a CAT(0) space) if and only if the quadrilateral cosine does not exceed one for every two pairs of
distinct points in . We also observe that a geodesically connected metric space is an domain if and only if, for every quadruple of points in , the quadrilateral inequality (known as Euler’s inequality in ) holds. As a corollary of our main result we give necessary and sufficient conditions for a semimetric space to be an domain. Our results provide a complete solution to the Curvature Problem posed by Gromov in the context of metric spaces
of non-positive curvature.
相似文献
8.
It is shown that an elliptic scattering operator A on a compact manifold with boundary with operator valued coefficients in the morphisms of a bundle of Banach spaces of class
() and Pisier’s property (α) has maximal regularity (up to a spectral shift), provided that the spectrum of the principal symbol
of A on the scattering cotangent bundle avoids the right half-plane. This is accomplished by representing the resolvent in terms
of pseudodifferential operators with -bounded symbols, yielding by an iteration argument the -boundedness of λ(A−λ)−1 in for some . To this end, elements of a symbolic and operator calculus of pseudodifferential operators with -bounded symbols are introduced. The significance of this method for proving maximal regularity results for partial differential
operators is underscored by considering also a more elementary situation of anisotropic elliptic operators on with operator valued coefficients. 相似文献
9.
Yonutz V. Stanchescu 《Combinatorica》2008,28(3):343-355
We describe the structure of three dimensional sets of lattice points, having a small doubling property. Let be a finite subset of ℤ3 such that dim = 3. If and , then lies on three parallel lines. Moreover, for every three dimensional finite set that lies on three parallel lines, if , then is contained in three arithmetic progressions with the same common difference, having together no more than terms. These best possible results confirm a recent conjecture of Freiman and cannot be sharpened by reducing the quantity
υ or by increasing the upper bounds for . 相似文献
10.
We study permanence properties of the classes of stable and so-called -stable -algebras, respectively. More precisely, we show that a (X)-algebra A is stable if all its fibres are, provided that the underlying compact metrizable space X has finite covering dimension or that the Cuntz semigroup of A is almost unperforated (a condition which is automatically satisfied for -algebras absorbing the Jiang–Su algebra tensorially). Furthermore, we prove that if is a K
1-injective strongly self-absorbing -algebra, then A absorbs tensorially if and only if all its fibres do, again provided that X is finite-dimensional. This latter statement generalizes results of Blanchard and Kirchberg. We also show that the condition
on the dimension of X cannot be dropped. Along the way, we obtain a useful characterization of when a -algebra with weakly unperforated Cuntz semigroup is stable, which allows us to show that stability passes to extensions of
-absorbing -algebras.
Research supported by: Deutsche Forschungsgemeinschaft (through the SFB 478), by the EU-Network Quantum Spaces - Noncommutative
Geometry (Contract No. HPRN-CT-2002-00280), and by the Center for Advanced Studies in Mathematics at Ben-Gurion University 相似文献
11.
John P. Steinberger 《Results in Mathematics》2008,51(3-4):319-338
If is any ring or semi-ring (e.g., ) and G is a finite abelian group, two elements a, b of the group (semi-)ring are said to form a factorization of G if ab = rΣ
g∈G
g for some . A factorization is called quasiperiodic if there is some element g ∈ G of order m > 1 such that either a or b – say b – can be written as a sum b
0 + ... + b
m−1 of m elements of such that ab
h
= g
h
ab
0 for h = 0, ... , m − 1. Hajós [5] conjectured that all factorizations are quasiperiodic when and r = 1 but Sands [15] found a counterexample for the group . Here we show however that all factorizations of abelian groups are quasiperiodic when and that all factorizations of cyclic groups or of groups of the type are quasiperiodic when . We also give some new examples of non-quasiperiodic factorizations with for the smaller groups and .
Received: May 12, 2006. Revised: October 3, 2007. 相似文献
12.
William E. Hornor 《Complex Analysis and Operator Theory》2007,1(4):549-569
We develop a translation-type model for univalent self-maps φ of the unit disc having an interior fixed-point and use the model to classify the φ-invariant measures on . We are particularly interested in maps which can be embedded in continuous semigroups of holomorphic self-maps of .
Received: February 2, 2007. Revised: June 18, 2007. Accepted: July 4, 2007. 相似文献
13.
Sven Kosub 《Mathematics in Computer Science》2008,1(3):487-505
A complete classification of the computational complexity of the fixed-point existence problem for Boolean dynamical systems,
i.e., finite discrete dynamical systems over the domain {0, 1}, is presented. For function classes and graph classes , an ()-system is a Boolean dynamical system such that all local transition functions lie in and the underlying graph lies in . Let be a class of Boolean functions which is closed under composition and let be a class of graphs which is closed under taking minors. The following dichotomy theorems are shown: (1) If contains the self-dual functions and contains the planar graphs, then the fixed-point existence problem for ()-systems with local transition function given by truth-tables is NP-complete; otherwise, it is decidable in polynomial time.
(2) If contains the self-dual functions and contains the graphs having vertex covers of size one, then the fixed-point existence problem for ()-systems with local transition function given by formulas or circuits is NP-complete; otherwise, it is decidable in polynomial
time.
相似文献
14.
Wenbin Guo 《manuscripta mathematica》2008,127(2):139-150
Let G be a finite group and a formation of finite groups. We say that a subgroup H of G is -supplemented in G if there exists a subgroup T of G such that G = TH and is contained in the -hypercenter of G/H
G
. In this paper, we use -supplemented subgroups to study the structure of finite groups. A series of previously known results are unified and generalized.
Research of the author is supported by a NNSF grant of China (Grant #10771180). 相似文献
15.
Haïkel Skhiri 《Integral Equations and Operator Theory》2008,62(1):137-148
Let be the algebra of all bounded linear operators on a complex Banach space X and γ(T) be the reduced minimum modulus of operator . In this work, we prove that if , is a surjective linear map such that is an invertible operator, then , for every , if and only if, either there exist two bijective isometries and such that for every , or there exist two bijective isometries and such that for every . This generalizes for a Banach space the Mbekhta’s theorem [12].
相似文献
16.
We study the C
*-algebra generated by Toeplitz operators with piece-wise continuous symbols acting on the Bergman space on the unit disk in . We describe explicitly each operator from this algebra and characterize Toeplitz operators which belong to the algebra.
To the memory of G. S. Litvinchuk 相似文献
17.
Valentina S. Harizanov Carl G. JockuschJr. Julia F. Knight 《Archive for Mathematical Logic》2009,48(1):39-53
We study the complexity of infinite chains and antichains in computable partial orderings. We show that there is a computable
partial ordering which has an infinite chain but none that is or , and also obtain the analogous result for antichains. On the other hand, we show that every computable partial ordering
which has an infinite chain must have an infinite chain that is the difference of two sets. Our main result is that there is a computably axiomatizable theory K of partial orderings such that K has a computable model with arbitrarily long finite chains but no computable model with an infinite chain. We also prove
the corresponding result for antichains. Finally, we prove that if a computable partial ordering has the feature that for every , there is an infinite chain or antichain that is relative to , then we have uniform dichotomy: either for all copies of , there is an infinite chain that is relative to , or for all copies of , there is an infinite antichain that is relative to . 相似文献
18.
It has been known for a long time that the Deligne–Lusztig curves associated to the algebraic groups of type and defined over the finite field all have the maximum number of -rational points allowed by the Weil “explicit formulas”, and that these curves are -maximal curves over infinitely many algebraic extensions of . Serre showed that an -rational curve which is -covered by an -maximal curve is also -maximal. This has posed the problem of the existence of -maximal curves other than the Deligne–Lusztig curves and their -subcovers, see for instance Garcia (On curves with many rational points over finite fields. In: Finite Fields with Applications
to Coding Theory, Cryptography and Related Areas, pp. 152–163. Springer, Berlin, 2002) and Garcia and Stichtenoth (A maximal
curve which is not a Galois subcover of the Hermitan curve. Bull. Braz. Math. Soc. (N.S.) 37, 139–152, 2006). In this paper, a positive answer to this problem is obtained. For every q = n
3 with n = p
r
> 2, p ≥ 2 prime, we give a simple, explicit construction of an -maximal curve that is not -covered by any -maximal Deligne–Lusztig curve. Furthermore, the -automorphism group Aut has size n
3(n
3 + 1)(n
2 − 1)(n
2 − n + 1). Interestingly, has a very large -automorphism group with respect to its genus .
Research supported by the Italian Ministry MURST, Strutture geometriche, combinatoria e loro applicazioni, PRIN 2006–2007. 相似文献
19.
The Stokes operator in weighted Lq-spaces II: weighted resolvent estimates and maximal Lp-regularity 总被引:1,自引:0,他引:1
Andreas Fr?hlich 《Mathematische Annalen》2007,339(2):287-316
In this paper we establish a general weighted L
q
-theory of the Stokes operator in the whole space, the half space and a bounded domain for general Muckenhoupt weights . We show weighted L
q
-estimates for the Stokes resolvent system in bounded domains for general Muckenhoupt weights. These weighted resolvent estimates
imply not only that the Stokes operator generates a bounded analytic semigroup but even yield the maximal L
p
-regularity of in the respective weighted L
q
-spaces for arbitrary Muckenhoupt weights . This conclusion is archived by combining a recent characterisation of maximal L
p
-regularity by -bounded families due to Weis [Operator-valued Fourier multiplier theorems and maximal L
p
-regularity. Preprint (1999)] with the fact that for L
q
-spaces -boundedness is implied by weighted estimates. 相似文献
20.
Ilwoo Cho 《Complex Analysis and Operator Theory》2007,1(3):367-398
We identify two noncommutative structures naturally associated with countable directed graphs. They are formulated in the
language of operators on Hilbert spaces. If G is a countable directed graphs with its vertex set V(G) and its edge set E(G), then we associate partial isometries to the edges in E(G) and projections to the vertices in V(G). We construct a corresponding von Neumann algebra
as a groupoid crossed product algebra
of an arbitrary fixed von Neumann algebra M and the graph groupoid
induced by G, via a graph-representation (or a groupoid action) α. Graph groupoids are well-determined (categorial) groupoids. The graph
groupoid
of G has its binary operation, called admissibility. This
has concrete local parts
, for all e ∈ E(G). We characterize
of
, induced by the local parts
of
, for all e ∈ E(G). We then characterize all amalgamated free blocks
of
. They are chracterized by well-known von Neumann algebras: the classical group crossed product algebras
, and certain subalgebras
(M) of operator-valued matricial algebra
. This shows that graph von Neumann algebras identify the key properties of graph groupoids.
Received: December 20, 2006. Revised: March 07, 2007. Accepted: March 13, 2007. 相似文献