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1.
The set of all first degree polynomials must be added to theset of approximations of the form a + b log (1 + cx) in orderthat a best Chebyshev approximation exist to all continuousfunctions on [0, ]. Best approximations in this augmented familyof approximations are characterized by alternation of theirerror curve and are unique. The Chebyshev operator is continuousat f if f is an approximant or f has a non-constant best approximation. 相似文献
2.
Let G be a graph of order 2n + l having maximum degree 2n –1. We prove that the total chromatic number of G is 2n if andonly if e + ' n, where w is a vertex of minimum degree in G, is the complement of G —w, e is the size of , and ' is the edge independence number of . 相似文献
3.
In this paper, a natural R
+
n+1
extension of singular integrals, i.e.,T
κ:f→K*φ
t
*t with K a standard C-Z kernel and ϕ usual one, is investigated. One of the main results is: Let (dμ, udx) ∈C1 and u-Mw, w∈A∞, then Tk is of type (Lp(udx), Lp(dμ)). As a related topic, a maximal operator
is proved to be of type
, where
, provided (dμ, udx) ∈C1 and u∈ A∞.
Supported by National Science Foundation of China 相似文献
4.
Glyn Harman 《Archiv der Mathematik》2008,90(3):239-245
Let P
+(m) denote the greatest prime factor of the positive integer m. Improving and simplifying work of Dartyge [3] we show that
for . Here improves on the previous exponent .
Received: 20 April 2007 相似文献
5.
For l, an -triangulation F of a planar domain is such that,for every T F, there holds 1 RT/2rT , where RT (resp. rT)denotes the radius of the circumscribed (resp. inscribed) circleof the triangle T. When T is varying in F the centre of itsinscribed circle is varying in a compact interior to T and itsorthogonal projections on the sides are varying in compact intervalsinterior to these sides. Precise results are given about thesizes of these compacts and are used for the computation oferror constants in the problem of Hermite interpolation by Powell-Sabinquadratic finite elements, bringing to the fore their dependenceon the parameter . 相似文献
6.
Raú l E. Curto Woo Young Lee 《Transactions of the American Mathematical Society》2005,357(12):4719-4737
In this paper we explore finite rank perturbations of unilateral weighted shifts . First, we prove that the subnormality of is never stable under nonzero finite rank perturbations unless the perturbation occurs at the zeroth weight. Second, we establish that 2-hyponormality implies positive quadratic hyponormality, in the sense that the Maclaurin coefficients of are nonnegative, for every , where denotes the orthogonal projection onto the basis vectors . Finally, for strictly increasing and 2-hyponormal, we show that for a small finite-rank perturbation of , the shift remains quadratically hyponormal.
7.
If = {1, 2, ..., s}, where 1 2 ... s > 0, is a partitionof n then denotes the associated irreducible character of Sn,the symmetric group on {1, 2, ..., n}, and, if cCSn, the groupalgebra generated by C and Sn, then dc(·) denotes thegeneralized matrix function associated with c. If c1, c2 CSnthen we write c1 c2 in case (A) (A) for each n x n positivesemi-definite Hermitian matrix A. If cCSn and c(e) 0, wheree denotes the identity in Sn, then or denotes (c(e))–1 c. The main result, an estimate for the norms of tensors of a certainanti-symmetry type, implies that if = {1, 2, ..., s, 1t} isa partition of n such that s > 1 and s = 2, and ' denotes{1, 2, ..., s-1, 1t} then (, {2}) where denotes characterinduction from Sn–2 x S2 to Sn. This in turn implies thatif = {1, 2, ..., s, 1t} with s > 1, s = 2, and ßdenotes {1 + 2, 2, ..., s-1, 1t} then ß which,in conjunction with other known results, provides many new inequalitiesamong immanants. In particular it implies that the permanentfunction dominates all normalized immanants whose associatedpartitions are of rank 2, a result which has proved elusivefor some years. We also consider the non-relationship problem for immanants– that is the problem of identifying pairs, (,ß)such that ß and ß are both false. 相似文献
8.
Let be a weight sequence of positive real numbers and let be a subnormal weighted shift with a weight sequence . Consider an extended weight sequence with and let 0: W_{\alpha (x)} \text{is} k \text{-hyponormal}\}$">for , where is the set of natural numbers. We obtain a formula to find the interval , which provides several examples to distinguish the classes of -hyponormal operators from one another.
9.
Raú l E. Curto Woo Young Lee 《Proceedings of the American Mathematical Society》2003,131(8):2479-2489
For , let be a collection of () positive weights. The Quadratically Hyponormal Completion Problem seeks necessary and sufficient conditions on to guarantee the existence of a quadratically hyponormal unilateral weighted shift with as the initial segment of weights. We prove that admits a quadratically hyponormal completion if and only if the self-adjoint matrix
is positive and invertible, where , , , , , and, for notational convenience, . As a particular case, this result shows that a collection of four positive numbers always admits a quadratically hyponormal completion. This provides a new qualitative criterion to distinguish quadratic hyponormality from 2-hyponormality.
is positive and invertible, where , , , , , and, for notational convenience, . As a particular case, this result shows that a collection of four positive numbers always admits a quadratically hyponormal completion. This provides a new qualitative criterion to distinguish quadratic hyponormality from 2-hyponormality.
10.
Stephan Ramon Garcia 《Proceedings of the American Mathematical Society》2005,133(10):3047-3056
We study the backward shift operator on Hilbert spaces (for ) which are norm equivalent to the Dirichlet-type spaces . Although these operators are unitarily equivalent to the adjoints of the forward shift operator on certain weighted Bergman spaces, our approach is direct and completely independent of the standard Cauchy duality. We employ only the classical Hardy space theory and an elementary formula expressing the inner product on in terms of a weighted superposition of backward shifts.
11.
A method is developed for evaluating Fourier integrals of theform A() = 11f(x) efax dx, 0. The method consists of expanding the function f in a seriesof Chebyshev polynomials and expressing the integral A() asa series of the Bessel functionsJr+(), r= 0, 1, 2,.... A partialsum AN() of the series provides an approximant to A(). The principalfeature of the method is that one set of N+1 evaluations off(x) suffices for the calculation of AN() for all , and alsothe truncation error A()AN() is essentially independentof . Numerical tests show that the method is accurate, economicaland reliable. An application to the inversion of Fourier andLaplace transforms is briefly described. 相似文献
12.
Smoothness of Holonomies for Codimension 1 Hyperbolic Dynamics 总被引:2,自引:0,他引:2
Hyperbolic invariant sets of C1+ diffeomorphisms where eitherthe stable or unstable leaves are 1-dimensional are consideredin this paper. Under the assumption that the has local productstructure, the authors prove that the holonomies between the1-dimensional leaves are C1+ for some 0 < < 1. 相似文献
13.
We present a new proof that the irreducible representationsof the von Neumann algebra generated by a strongly continuoussemigroup of partial isometries of index 1 are unique up toequivalence, as well as a proof that when such an algebra isa factor, its representations are completely reducible. As anapplication, we show that the irreducible representations ofa strongly continuous semigroup of isometries {U(), 0} suchthat are equivalent. 相似文献
14.
Let be an ideal in a Noetherian local ring . Then the sequence is -regular if every is a non-zerodivisor in and if for all integers , where runs over the elements of the set .
15.
A special Pisot number is a Pisot number such that /(1)is also a Pisot number. Lagarias, Porta and Stolarsky found11 special Pisot numbers. Here it is proved that there are nomore. Also, the one known Salem number with the property that/(1) is a Pisot number is shown to be the only such number.1991 Mathematics Subject Classification 11R06. 相似文献
16.
Positive Eigenfunctions of a Schrodinger Operator 总被引:1,自引:0,他引:1
The paper considers the eigenvalue problem
where , and
for some bounded open set RN. Given >0, does there exist a value of >0 for which theproblem has a positive solution? It is shown that this occursif and only if lies in a certain interval (,1) and that inthis case the value of is unique, =(). The properties of thefunction () are also discussed. 相似文献
17.
In 1940 Nisnevi published the following theorem [3]. Let (G) be a family of groups indexed by some set and (F) a family of fields of the same characteristic p0. Iffor each the group G has a faithful representation of degreen over F then the free product* G has a faithful representationof degree n+1 over some field of characteristic p. In [6] Wehrfritzextended this idea. If (G) GL(n, F) is a family of subgroupsfor which there exists ZGL(n, F) such that for all the intersectionGF.1n=Z, then the free product of the groups *ZG with Z amalgamatedvia the identity map is isomorphic to a linear group of degreen over some purely transcendental extension of F. Initially, the purpose of this paper was to generalize theseresults from the linear to the skew-linear case, that is, togroups isomorphic to subgroups of GL(n, D) where the D are divisionrings. In fact, many of the results can be generalized to ringswhich, although not necessarily commutative, contain no zero-divisors.We have the following. 相似文献
18.
Lanczos (1952) claims that expansion of a function in a seriesof Chebyshev polynomials is usually superior to expansion ina series of ultraspherical polynomials for any possible non-zerovalue of the parameter . We look for conditions on the functionunder which this superiority can be proved and measured; weachieve some success on the assumption that is positive, butthe results for negative are less satisfactory. 相似文献
19.
Some recovery type error estimators for linear finite elements are analyzed under 0)$"> regular grids. Superconvergence of order is established for recovered gradients by three different methods. As a consequence, a posteriori error estimators based on those recovery methods are asymptotically exact.
20.
We show how to construct an asymptotic solution to the delayedlogistic equation = y(1y1), corresponding to the asymptoticlimit . The results of the analysis are compared with a numericalcomputation, and found to be comparatively accurate for >2. Since the approach adopted is novel, we comment on some featureswhich may be relevant in other problems. 相似文献