of step two to another such group satisfies a Beltrami-type system of partial differential equations which is usually not elliptic but subelliptic when the group
is strongly 2-pseudoconcave. We derive an integral representation formula for CR-mappings from a strongly 2-pseudoconcave nilpotent Lie group of step two to another such group and establish the Hölder continuity of ε-quasi-CR-mappings and the stability of CR-mappings between such groups.
This addendum to [1] completely characterizes the boundedness and compactness of a recently introduced integral type operator from the space of bounded holomorphic functions H∞(\(\mathbb{D}^n \)) on the unit polydisk \(\mathbb{D}^n \) to the mixed norm space
with p, q ∈ [1,∞) and α = (α1, ..., αn) such that αj > ?1 for every j = 1, ..., n. We show that the operator is bounded if and only if it is compact and if and only if g ∈
, and the aαjk and pjk are constants, x ∈ Ω, and Ω is a bounded open set. The boundary conditions correspond to the Dirichlet problem. Let N±(μ) be the positive and negative spectral counting functions. We establish the asymptotics N±(μ) ～ (mesmΩ)φ±(μ) as μ → +0. The functions φ±(μ) are independent of Ω. In the nonelliptic case, these asymptotics are in general different from the classical (Weyl) asymptotics.
, this coincides with the notion of a Jordan ideal.) We study conditions under which Jordan submodules are subbimodules. General criteria are given in the purely algebraic situation as well as for the case of Banach bimodules over Banach algebras. We also consider symmetrically normed Jordan submodules over C*-algebras. It turns out that there exist C*-algebras in which not all Jordan ideals are ideals.
We construct complete noncompact Riemannian metrics with G2-holonomy on noncompact orbifolds that are ?3-bundles with the twistor space Open image in new window as a spherical fiber. 相似文献
in the space of analytic functions on the unit polydisk Un in the complex vector space ?n. We show that the operator is bounded in the mixed norm space
, with p, q ∈ [1, ∞) and α = (α1, …, αn), such that αj > ?1, for every j = 1, …, n, if and only if \(\sup _{z \in U^n } \prod\nolimits_{j = 1}^n {\left( {1 - \left| {z_j } \right|} \right)} \left| {g(z)} \right| < \infty \). Also, we prove that the operator is compact if and only if \(\lim _{z \to \partial U^n } \prod\nolimits_{j = 1}^n {\left( {1 - \left| {z_j } \right|} \right)} \left| {g(z)} \right| = 0\).
A subgroup H of a group G is called weakly s-permutable in G if there is a subnormal subgroup T of G such that G = HT and H ∩ T ≤ HsG, where HsG is the maximal s-permutable subgroup of G contained in H. We improve a nice result of Skiba to get the following
Theorem. Let ? be a saturated formation containing the class of all supersoluble groups
and let G be a group with E a normal subgroup of G such that G/E ∈ ?. Suppose that each noncyclic Sylow p-subgroup P of F*(E) has a subgroup D such that 1 < |D| < |P| and all subgroups H of P with order |H| = |D| are weakly s-permutable in G for all p ∈ π(F*(E)); moreover, we suppose that every cyclic subgroup of P of order 4 is weakly s-permutable in G if P is a nonabelian 2-group and |D| = 2. Then G ∈ ?.
It is well-known that Morgan-Voyce polynomials Bn(x) and bn(x) satisfy both a Sturm-Liouville equation of second order and a three-term recurrence equation ([SWAMY, M.: Further properties of Morgan-Voyce polynomials, Fibonacci Quart. 6 (1968), 167–175]). We study Diophantine equations involving these polynomials as well as other modified classical orthogonal polynomials with this property. Let A, B, C ∈ ? and {pk(x)} be a sequence of polynomials defined by
∈ ?d (d ≥ 1) is considered. The simultaneous distribution of the pair is specified in the form that is common for analogous problems in various fields. It has the form
) is constructed using a realization of an auxiliary Markov sequence of trial pairs. Applications of this method in particle transport theory and in kinetics of rarefied gases are discussed.
A theorem of Baker says that a function F entire on ?d such that F(?d) ? ? and increasing slower (in a precise sense) than \(2^{z_1 + \cdots + z_d } \) is necessarily a polynomial. This is a multivariate generalisation of the celebrated theorem of Pólya (case d = 1). Using the theory of analytic functionals with non-compact carrier, Yoshino proved a general theorem dealing with the growth of arithmetic analytic functions, which implies that the conclusion of Baker’s theorem holds if F is only assumed to be holomorphic on the domain
The case d = 1 was also treated in a different way by Gel’fond and Pólya by means of the characteristic function of Carlson-Nörlund. This function was introduced to bound in a nearly optimal way the growth of holomorphic functions of one variable that can be expanded in a Newton interpolation series in the half-plane
that can be expanded in multiple Newton series. These considerations enable us to improve Gel’fond-Pólya’s and Yoshino’s theorems, in particular, to remove or to weaken certain of their technical conditions.
of simplicial complexes G, we introduce the notion of a
-C-space. In the definition of a C-space, open disjoint families vi refine coverings ui. The nerves of these families are zero-dimensional complexes. In our definition, the nerve of a family vi must embed in the complex Gi of the class
. We give a complete characterization of bicompact
Let a function f : \(\Pi ^{ * ^m } \) → ? be Lebesgue integrable on \(\Pi ^{ * ^m } \) and Riemann-Stieltjes integrable with respect to a function G : \(\Pi ^{ * ^m } \) → ? on \(\Pi ^{ * ^m } \). Then the Parseval equality
χk(x) dG(x) are Fourier coefficients of the function f and Fourier-Stieltjes coefficients of the function G with respect to the Haar system, respectively; the integrals in the equality and in the definition of the coefficients of the function G are the Riemann-Stieltjes integrals; the series in the right-hand side of the equality converges in the sense of rectangular partial sums; and the overline indicates the complex conjugation. If f : Πm → ? is a complex-valued Lebesgue integrable function, G is a complex-valued function of bounded variation on Πm,
holds for almost all x ∈ \(\Pi ^{ * ^m } \) in the sense of any summation method with respect to which the Fourier series of Lebesgue integrable functions are summable to these functions almost everywhere (the integral here is interpreted in the sense of Lebesgue-Stieltjes).
In this paper, using an equivalent characterization of the Besov space by its wavelet coefficients and the discretization technique due to Maiorov, we determine the asymptotic degree of the Bernstein n-widths of the compact embeddings Bq0s＋t（Lp0（Ω））→Bq1s（Lp1（Ω））, t〉max{d（1/p0-1/p1）, 0}, 1 ≤ p0, p1, q0, q1 ≤∞,where Bq0s＋t（Lp0（Ω）） is a Besov space defined on the bounded Lipschitz domain Ω ？ Rd. The results we obtained here are just dual to the known results of Kolmogorov widths on the related classes of functions. 相似文献
We construct an embedding Φ of [0, 1]∞ into Ham(M, ω), the group of Hamiltonian diffeomorphisms of a suitable closed symplectic manifold (M, ω). We then prove that Φ is in fact a quasi-isometry. After imposing further assumptions on (M, ω), we adapt our methods to construct a similar embedding of ? ⊕ [0, 1]∞ into either Ham(M, ω) or
, the universal cover of Ham(M, ω). Along the way, we prove results related to the filtered Floer chain complexes of radially symmetric Hamiltonians. Our proofs rely heavily on a continuity result for barcodes (as presented in [28]) associated to filtered Floer homology viewed as a persistence module.
Let r≥2 be an integer. A real number α ∈ [0,1) is a jump for r if for any Open image in new window >0 and any integer m, m≥r, any r-uniform graph with n>n0( Open image in new window ,m) vertices and at least Open image in new window edges contains a subgraph with m vertices and at least Open image in new window edges, where c=c(α) does not depend on Open image in new window and m. It follows from a theorem of Erd?s, Stone and Simonovits that every α ∈ [0,1) is a jump for r=2. Erd?s asked whether the same is true for r≥3. Frankl and Rödl gave a negative answer by showing that Open image in new window is not a jump for r if r≥3 and l>2r. Following a similar approach, we give several sequences of non-jumping numbers generalizing the above result for r=4. 相似文献
