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 ∈
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
, 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.
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.
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 ∈ ?.
over the Grassmannian manifolds G(n, p) as noncompact symmetric affine spaces together with their Cartan model in the group of the Euclidean motions SE(n).
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
In the present paper a generalized Kählerian space Open image in new window of the first kind is considered as a generalized Riemannian space \(\mathbb{G}\mathbb{R}_N \) with almost complex structure Fih that is covariantly constant with respect to the first kind of covariant derivative.Using a non-symmetric metric tensor we find necessary and sufficient conditions for geodesic mappings f: Open image in new window with respect to the four kinds of covariant derivatives. These conditions have the form of a closed system of partial differential equations in covariant derivatives with respect to unknown components of the metric tensor and the complex structure of the Kählerian space Open image in new window . 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.
We discuss the relationship between the strong asymptotic equivalence relation and the generalized inverse in the class of all nondecreasing and unbounded functions, defined and positive on a half-axis [a, +∞) (a > 0). In the main theorem, we prove a proper characterization of the function class IRV∩, where IRV is the class of all -regularly varying functions (in the sense of Karamata) having continuous index function. 相似文献
We consider the problem of optimal boundary control of string vibrations by a displacement at one endpoint with the other endpoint being fixed; the problem is considered in the space
, p ≥ 1. The control brings the vibration process from the quiescent state to an arbitrarily prescribed state in a time that is a multiple of the double string length.
Results on the solvability of boundary integral equations on a plane contour with a peak obtained in collaboration with V.G. Maz’ya are developed. Earlier, it was proved that, on a contour Γ with an outward peak, the operator of the boundary equation of the Dirichlet boundary value problem maps the space ?p, β + 1 (Γ) continuously onto \(\mathcal{N}_{p,\beta } (\Gamma )\). The norm of a function in ?p, β (Γ) is defined as
, where q± are the intersection points of Γ with the circle {z: |z| = |q|} and δ > 0 is a fixed small number. On a contour with an inward peak, the operator of the boundary equation of the Dirichlet problem continuously maps ?p, β + 1 (Γ) onto ?p, β(Γ), where ?p, β(Γ) is the direct sum of \(\mathcal{N}_{p,\beta }^ + (\Gamma )\) (Γ) and the space
(Γ) of functions on Γ of the form p(z) = Σk = 0mt(k)Rezk with the parameter m = [μ ? β ? p?1]. The operator I ? 2W of the boundary integral equation of plane elasticity theory, where W is the elastic double-layer potential, is considered. The main result is that the operator I ? 2W continuously maps the space ?p, β + 1 × ?p, β + 1(Γ) to the space \(\mathcal{N}_{p,\beta }^ - \times \mathcal{N}_{p,\beta }^ - (\Gamma )\).
On a contour with an inward peak, the obtained representation of the operator I ? 2W and theorems on the boundedness of auxiliary integral operators imply that the images of vector-valued functions from ?p, β + 1 × ?p, β + 1(Γ) have components representable as sums of functions from the spaces \(\mathcal{N}_{p,\beta }^ - (\Gamma )\)(Γ) and ?p, β(Γ). 相似文献
Under study is the category of the possibly noncommutative H-module algebras that are mapped homomorphically onto commutative algebras. The H-equivariant Martindale ring of quotients QH(A) is shown to be a finite-dimensional Frobenius algebra over the subfield of invariant elements QH(A)H and also the classical ring of quotients for A. We introduce a full subcategory of such that the algebras in are integral over its subalgebras of invariants and construct a functor ?? , which is left adjoined to the inclusion ?? . 相似文献
In this paper, we explore the fixed point theory of n-valued maps using configuration spaces and braid groups, focusing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the projective plane (resp. the 2-sphere S2) has the Wecken property for n-valued maps for all n ∈ ? (resp. all n ≥ 3). In the case n = 2 and S2, we prove a partial result about the Wecken property. We then describe the Nielsen number of a non-split n-valued map Open image in new window of an orientable, compact manifold without boundary in terms of the Nielsen coincidence numbers of a certain finite covering q: X? → X with a subset of the coordinate maps of a lift of the n-valued split map Open image in new window . 相似文献
Let \(\mathfrak{g} = W_1 \) be the Witt algebra over an algebraically closed field k of characteristic p > 3; and let Open image in new window be the commuting variety of g. In contrast with the case of classical Lie algebras of P. Levy [J. Algebra, 2002, 250: 473–484], we show that the variety Open image in new window is reducible, and not equidimensional. Irreducible components of Open image in new window and their dimensions are precisely given. As a consequence, the variety Open image in new window is not normal. 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 \(\lim _{z \to \partial U^n } \prod\nolimits_{j = 1}^n {\left( {1 - \left| {z_j } \right|} \right)} \left| {g(z)} \right| = 0\).
