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1.
The zero sets of (D+a)ng(t) with in the (t,a)-plane are investigated for and .The results are used to determine entire interpolations to functions , which give representations for the best approximation and best one-sided approximation from the class of functions of exponential type η>0 to . 相似文献
2.
Let be a bounded domain such that 0Ω. Denote by , the set of all complex polynomials of degree at most n. Let where . We relate the maximal polynomial range to the geometry of Ω. 相似文献
3.
Let p be a trigonometric polynomial, non-negative on the unit circle . We say that a measure σ on belongs to the polynomial Szegő class, if , σs is singular, andFor the associated orthogonal polynomials {n}, we obtain pointwise asymptotics inside the unit disc . Then we show that these asymptotics hold in L2-sense on the unit circle. As a corollary, we get an existence of certain modified wave operators. 相似文献
4.
We relate asymptotics of Jacobi parameters to asymptotics of the spectral weights near the edges. Typical of our results is that for an≡1, bn=−Cn−β (), one has on (−2,2), and near x=2, where 相似文献
5.
A family of orthonormal polynomials on the unit ball Bd of with respect to the inner productwhere Δ is the Laplace operator, is constructed explicitly. 相似文献
6.
Let be the usual Sobolev class of functions on the unit ball in , and be the subclass of all radial functions in . We show that for the classes and , the orders of best approximation by polynomials in coincide. We also obtain exact orders of best approximation in of the classes by ridge functions and, as an immediate consequence, we obtain the same orders in for the usual Sobolev classes . 相似文献
7.
For a graph property , the edit distance of a graph G from , denoted , is the minimum number of edge modifications (additions or deletions) one needs to apply to G in order to turn it into a graph satisfying . What is the largest possible edit distance of a graph on n vertices from ? Denote this distance by .A graph property is hereditary if it is closed under removal of vertices. In a previous work, the authors show that for any hereditary property, a random graph essentially achieves the maximal distance from , proving: with high probability. The proof implicitly asserts the existence of such , but it does not supply a general tool for determining its value or the edit distance.In this paper, we determine the values of and for some subfamilies of hereditary properties including sparse hereditary properties, complement invariant properties, (r,s)-colorability and more. We provide methods for analyzing the maximum edit distance from the graph properties of being induced H-free for some graphs H, and use it to show that in some natural cases G(n,1/2) is not the furthest graph. Throughout the paper, the various tools let us deduce the asymptotic maximum edit distance from some well studied hereditary graph properties, such as being Perfect, Chordal, Interval, Permutation, Claw-Free, Cograph and more. We also determine the edit distance of G(n,1/2) from any hereditary property, and investigate the behavior of as a function of p.The proofs combine several tools in Extremal Graph Theory, including strengthened versions of the Szemerédi Regularity Lemma, Ramsey Theory and properties of random graphs. 相似文献
8.
Let , with
-1=x0n<x1n<<xnn<xn+1,n=1