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1.
The commutator of the Kato square root for second order elliptic operators on ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>
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Let L=-div(A▽) be a second order divergence form elliptic operator, and A be an accretive, n×n matrix with bounded measurable complex coefficients in Rn. We obtain the Lp bounds for the commutator generated by the Kato square root √L and a Lipschitz function, which recovers a previous result of Calderón, by a different method. In this work, we develop a new theory for the commutators associated to elliptic operators with Lipschitz function. The theory of the commutator with Lipschitz function is distinguished from the analogous elliptic operator theory. 相似文献
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Josef Nagel 《Monatshefte für Mathematik》1983,95(1):33-44
The Kantorovi? operators of second order are introduced byQ n f= =(B n+2 F)″ whereF is the double indefinite integraloff andB n+2 the (n+2)-th Bernstein operator. The operatorsQ n will reveal a close affinity to the so-called modified Bernstein operatorsC n introduced bySchnabl [10] on a quite different way. The article contains investigations concerning the asymptotic behavior ofQ n kn f (asn → ∞), where (k n) is a sequence of natural numbers. 相似文献
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Ronald E. Mickens 《Journal of Difference Equations and Applications》2013,19(3):337-349
We extend a previous calculation on a Lindstedt Poincar'e type perturbation method to order ε2 for a class of nonlinear difference equations which come from a nonstandard finite difference scheme constructed for I-dim nonlinear oscillators. This procedure eliminates secular terms and leads to results that are uniformly valid. Arguments are given on the applicability of the method to higher orders of the perturbation expansion in the small parameter ε 相似文献
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We establish necessary and sufficient conditions under which the linear span of positive AM-compact operators (in the sense
of Fremlin) from a Banach lattice E into a Banach lattice F is an order σ-complete vector lattice. 相似文献
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Sourav Chatterjee 《Probability Theory and Related Fields》2009,143(1-2):1-40
Linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems. The proofs of such results are usually rather difficult, involving hard computations specific to the model in question. In this article we attempt to formulate a unified technique for deriving such results via relatively soft arguments. In the process, we introduce a notion of ‘second order Poincaré inequalities’: just as ordinary Poincaré inequalities give variance bounds, second order Poincaré inequalities give central limit theorems. The proof of the main result employs Stein’s method of normal approximation. A number of examples are worked out, some of which are new. One of the new results is a CLT for the spectrum of gaussian Toeplitz matrices. 相似文献
8.
V. E. Adler 《Functional Analysis and Its Applications》2016,50(4):257-267
We solve the classification problem for integrable lattices of the form u, t = f(u ?2,..., u 2) under the additional assumption of invariance with respect to the group of linear-fractional transformations. The obtained list contains five equations, including three new ones. Difference Miura-type substitutions are found, which relate these equations to known polynomial lattices. We also present some classification results for generic lattices. 相似文献
9.
The character degree graph of a finite group G is the graph whose vertices are the prime divisors of the irreducible character degrees of G and two vertices p and q are joined by an edge if pq divides some irreducible character degree of G. It is proved that some simple groups are uniquely determined by their orders and their character degree graphs. But since the character degree graphs of the characteristically simple groups are complete, there are very narrow class of characteristically simple groups which are characterizable by this method.We prove that the characteristically simple group A5 × A5 is uniquely determined by its order and its character degree graph. We note that this is the first example of a non simple group which is determined by order and character degree graph. As a consequence of our result we conclude that A5 × A5 is uniquely determined by its complex group algebra. 相似文献
10.
A few years ago Kramer and Laubenbacher introduced a discrete notion of homotopy for simplicial complexes. In this paper, we compute the discrete fundamental group of the order complex of the Boolean lattice. As it turns out, it is equivalent to computing the discrete homotopy group of the 1-skeleton of the permutahedron. To compute this group we introduce combinatorial techniques that we believe will be helpful in computing discrete fundamental groups of other polytopes. More precisely, we use the language of words, over the alphabet of simple transpositions, to obtain conditions that are necessary and sufficient to characterize the equivalence classes of cycles. The proof requires only simple combinatorial arguments. As a corollary, we also obtain a combinatorial proof of the fact that the first Betti number of the complement of the 3-equal arrangement is equal to 2 n?3(n 2?5n+8)?1. This formula was originally obtained by Björner and Welker in 1995. 相似文献
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We develop a theory of second order diffusion processes and associated stochastic differential equations of second order. We show that equations of evolution of the density, mean velocity and momentum flux are a family of first order conservation laws similar to those of continuum mechanics. We verify that the theory is satisfied for a large class of reciprocal Gaussian processes 相似文献
12.
Emily J. King Maria A. Skopina 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(3):222-231
With an eye on applications in quantum mechanics and other areas of science, much work has been done to generalize traditional
analytic methods to p-adic systems. In 2002 the first paper on p-adic wavelets was published. Since then p-adic wavelet sets, multiresolution analyses, and wavelet frames have all been introduced. However, so far all constructions
have involved dilations by p. This paper presents the first construction of a p-adic wavelet system with a more general matrix dilation, laying the foundation for further work in this direction. 相似文献
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Kwang Ho SHON 《中国科学A辑(英文版)》2007,50(6):786-800
In this paper, we investigate the existence and the form of subnormal solution for a class of second order periodic linear differential equations, estimate the growth properties of all solutions, and answer the question raised by Gundersen and Steinbart. 相似文献
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The classical Hardy-Littlewood-Sobolev theorems for Riesz potentials (-Δ) -α/2 are extended to the generalised fractional integrals L-α/2 for 0 < α < n, where L =-div A is a uniformly complex elliptic operator with bounded measurable coefficients in Rn. 相似文献
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Let M n(n ≥ 2) be an immersed umbilic-free hypersurface in the (n+1)-dimensional unit sphere S n+1. Then M n is associated with a so-called Möbius metric g, and a Möbius second fundamental form B which are invariants of M nunder the Möbius transformation group of S n+1. In this paper, we classify all umbilic-free hypersurfaces with parallel Möbius second fundamental form. 相似文献
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Linda Brown Westrick 《Israel Journal of Mathematics》2017,219(1):431-448
A family of sets is union-free if there are no three distinct sets in the family such that the union of two of the sets is equal to the third set. Kleitman proved that every union-free family has size at most (1+o(1))( n/2 n ). Later, Burosch–Demetrovics–Katona–Kleitman–Sapozhenko asked for the number α(n) of such families, and they proved that \({2^{\left( {\begin{array}{*{20}{c}} n \\ {n/2} \end{array}} \right)}} \leqslant \alpha \left( n \right) \leqslant {2^{2\sqrt 2 \left( {\begin{array}{*{20}{c}} n \\ {n/2} \end{array}} \right)\left( {1 + o\left( 1 \right)} \right)}}\) They conjectured that the constant \(2\sqrt 2 \) can be removed in the exponent of the right-hand side. We prove their conjecture by formulating a new container-type theorem for rooted hypergraphs. 相似文献
19.
On the Fekete and Szegö problem for starlike mappings of order <Emphasis Type="Italic">α</Emphasis>
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Let S α * be the familiar class of normalized starlike functions of order α in the unit disk. In this paper, we establish the Fekete and Szegö inequality for the class S α * , and then we generalize this result to the unit ball in a complex Banach space or on the unit polydisk in C n . 相似文献
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We obtain sharp coefficient bounds for some p-valent starlike functions of order β, 0 ≤ β < p. Initially this problem was handled by Aouf in [1]. We pointed out that the proof by Aouf is incorrect and present a correct proof. 相似文献