共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, three new discreteness criteria for Möbius groups acting on\(\bar R^{n * } \) are obtained; they are generalizations of known results using the information of two-generator subgroups. 相似文献
2.
Xavier Mary 《Semigroup Forum》2014,88(3):647-669
Inverse semigroups and orthodox semigroups are either defined in terms of inverses, or in terms of the set of idempotents E(S). In this article, we study analogs of these semigroups defined in terms of inverses modulo Green’s relation \(\mathcal{H}\) , or in terms of the set of completely regular elements H(S). Results are obtained both for the regular and the non-regular cases. We then study the interplays between these new classes of semigroups, as well as with various known classes notably of inverse, orthodox, E-solid and cryptic semigroups. 相似文献
3.
Dr. Bernhard Roider 《Monatshefte für Mathematik》1975,79(4):325-332
In Schwartz' terminology, a real or complex valued functionf, defined and infinitely differentiable on ? n , belongs to \(\mathfrak{O}_M \) iff, as well as any of its derivatives, is at most of polynomial growth. The topology of \(\mathfrak{O}_M \) is defined by the seminorms sup{∣?(x)D p f(x)∣;x∈? n }, where ? belongs to \(\mathfrak{S}\) andD p is any derivative. It is well-known that \(\mathfrak{O}_M \) is non-metrisable. For any μ: ? n →?, let \(\mathfrak{B}_\mu \) be the space of all infinitely differentiable functionsf satisfying, for eachp, sup{∣(1+∣x∣2)?μ(p) D p f(x)∣;x∈? n }<∞, with the obvious topology. These spaces, which are of very little use elsewhere in the theory of distributions, can be conveniently applied to characterise the metrisable linear subspaces of \(\mathfrak{O}_M \) : A linear subspace of \(\mathfrak{O}_M \) is metrisable if and only if it is, algebraically and topologically, a subspace of some \(\mathfrak{B}_\mu \) . 相似文献
4.
The Ramanujan Journal - We extend the results of Kaneko–Zagier and Baba–Granath on relations of supersingular polynomials and solutions of certain second-order modular differential... 相似文献
5.
Paul Shafer 《Archive for Mathematical Logic》2012,51(3-4):407-423
We prove Menger’s theorem for countable graphs in ${{\Pi^1_1\tt{-CA}_0}}$ . Our proof in fact proves a stronger statement, which we call extended Menger’s theorem, that is equivalent to ${{\Pi^1_1\tt{-CA}_0}}$ over ${{\tt{RCA}_0}}$ . 相似文献
6.
We show that for every sequence \({(p_n)_{n\in\mathbb{N}}}\) with 1 ≤ p n ≤ 2 there exists an \({\mathcal{L}_1}\) -space with the Radon-Nikodým containing an isomorphic copy of \({\ell_1(\ell_{p_n})}\) . 相似文献
7.
In this paper, we consider the Sturm–Liouville problem with spectral parameter in the boundary conditions. We associate this problem with a self-adjoint operator in the Pontryagin space \(\Pi _{2}\). Using this operator-theoretic formulation and analytic methods, we study the basis properties in the space \(L_{p} (0,1),\,1<p < \infty \), of systems of root functions of this problem. 相似文献
8.
Tóth János T. Filip Ferdinánd Bukor József Zsilinszky László 《Periodica Mathematica Hungarica》2021,82(2):125-135
Periodica Mathematica Hungarica - Let $$\mathbb N$$ be the set of positive integers, and denote by $$\begin{aligned} \lambda (A)=\inf \{t>0:\sum _{a\in A} a^{-t}<\infty \}... 相似文献
9.
In this article I study a number of topological and algebraic dimension type properties of simple C∗-algebras and their interplay. In particular, a simple C∗-algebra is defined to be (tracially) (m,[`(m)])(m,\bar{m})-pure, if it has (strong tracial) m-comparison and is (tracially) [`(m)]\bar{m}-almost divisible. These notions are related to each other, and to nuclear dimension. 相似文献
10.
In this paper, by using the “twisting technique” we obtain a class of new modules A b over the Witt algebras \(\mathcal {W}_{n}\) from modules A over the Weyl algebras \(\mathcal {K}_{n}\) (of Laurent polynomials) for any \(b\in \mathbb {C}\). We give necessary and sufficient conditions for A b to be irreducible, and determine necessary and sufficient conditions for two such irreducible \(\mathcal {W}_{n}\)-modules to be isomorphic. Since \(\mathfrak {sl}_{n+1}(\mathbb {C})\) is a subalgebra of \(\mathcal {W}_{n}\), all the above irreducible \(\mathcal {W}_{n}\)-modules A b can be considered as \(\mathfrak {sl}_{n+1}(\mathbb {C})\)-modules. For a class of such \(\mathfrak {sl}_{n+1}(\mathbb {C})\)-modules, denoted by Ω1?a (λ 1, λ 2, ? ,λ n ) where \(a\in \mathbb {C}, \lambda _{1},\lambda _{2},\cdots ,\lambda _{n} \in \mathbb {C}^{*}\), we determine necessary and sufficient conditions for these \(\mathfrak {sl}_{n+1}(\mathbb {C})\)-modules to be irreducible. If the \(\mathfrak {sl}_{n+1}(\mathbb {C})\)-module Ω1?a (λ 1, λ 2,? ,λ n ) is reducible, we prove that it has a unique nontrivial submodule W 1?a (λ 1, λ 2,...λ n ) and the quotient module is the finite dimensional \(\mathfrak {sl}_{n+1}(\mathbb {C})\)-module with highest weight mΛ n for some non-negative integer \(m\in \mathbb {Z}_{+}\). We also determine necessary and sufficient conditions for two \(\mathfrak {sl}_{n+1}(\mathbb {C})\)-modules of the form Ω1?a (λ 1, λ 2,? ,λ n ) or of the form W 1?a (λ 1, λ 2,...λ n ) to be isomorphic. 相似文献
11.
For any unital separable simple infinite-dimensional nuclear C ∗-algebra with finitely many extremal traces, we prove that -absorption, strict comparison and property (SI) are equivalent. We also show that any unital separable simple nuclear C ∗-algebra with tracial rank zero is approximately divisible, and hence is -absorbing. 相似文献
12.
N. V. Krylov 《Probability Theory and Related Fields》2010,147(3-4):583-605
We prove Itô’s formula for the L p -norm of a stochastic ${W^{1}_{p}}$ -valued processes appearing in the theory of SPDEs in divergence form. 相似文献
13.
The Aronszajn–Donoghue Theory for Rank One Perturbations of the
$$\mathcal{H}_{-2} {\text{-Class}}$$
A singular rank one perturbation
of a self-adjoint operator A in a Hilbert space
is considered, where
and
but
with
the usual A–scale of Hilbert spaces. A modified version of the Aronszajn-Krein formula is given. It has the form
where F denotes the regularized Borel transform of the scalar spectral measure of A associated with . Using this formula we develop a variant of the well known Aronszajn–Donoghue spectral theory for a general rank one perturbation of the
class.Submitted: March 14, 2002 Revised: December 15, 2002 相似文献
14.
Ansten Mørch Klev 《Archive for Mathematical Logic》2009,48(7):691-703
Using infinite time Turing machines we define two successive extensions of Kleene’s O{\mathcal{O}} and characterize both their height and their complexity. Specifically, we first prove that the one extension—which we will
call O+{\mathcal{O}^{+}}—has height equal to the supremum of the writable ordinals, and that the other extension—which we will call O++{\mathcal{O}}^{++}—has height equal to the supremum of the eventually writable ordinals. Next we prove that O+{\mathcal{O}^+} is Turing computably isomorphic to the halting problem of infinite time Turing computability, and that O++{\mathcal{O}^{++}} is Turing computably isomorphic to the halting problem of eventual computability. 相似文献
15.
S. Khoroshkin D. Lebede S. Pakuliak A. Stolin V. Tolstoy 《Compositio Mathematica》1999,115(2):185-204
The classical limit of the scaled elliptic algebra $\mathcal{A}$ ?,η ( $\widetilde{\mathfrak{s}\mathfrak{l}}_2$ ) is investigated. The limiting Lie algebra is described in two equivalent ways: as a central extension of the algebra of generalized automorphic sl2 valued functions on a strip and as an extended algebra of decreasing automorphic sl2 valued functions on the real line. A bialgebra structure and an infinite-dimensional representation in the Fock space are studied. The classical limit of elliptic algebra $\mathcal{A}$ q,p ( $\widetilde{\mathfrak{s}\mathfrak{l}}_2$ ) is also briefly presented. 相似文献
16.
In this paper, a general orthogonal transformation on the optimal quaternary sequence Families ${\mathcal{B}}$ and ${\mathcal{C}}$ is presented. Consequently, the known optimal Family ${\mathcal{D}}$ and a new optimal Family ${\mathcal{E}}$ are produced in a uniform method. In contrast to the known optimal Family ${\mathcal{D}}$ , the new Family ${\mathcal{E}}$ has the same parameters such as the sequence length 2(2 n ? 1), the family size 2 n , and the maximal nontrivial correlation value ${2^{\frac{n+1}{2}}+2}$ , where n is a positive integer, but with a different correlation function. 相似文献
17.
18.
Alessandro Chiodo David Eisenbud Gavril Farkas Frank-Olaf Schreyer 《Inventiones Mathematicae》2013,194(1):73-118
We formulate, and in some cases prove, three statements concerning the purity or, more generally, the naturality of the resolution of various modules one can attach to a generic curve of genus g and a torsion point of ? in its Jacobian. These statements can be viewed an analogues of Green’s Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space $\mathcal{R}_{g,\ell}$ of twisted level ? curves of genus g and use this to derive results about the birational geometry of $\mathcal{R}_{g, \ell}$ . For instance, we prove that $\mathcal{R}_{g,3}$ is a variety of general type when g>11 and the Kodaira dimension of $\mathcal{R}_{11,3}$ is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2. 相似文献
19.
Aaron Peterson 《Archiv der Mathematik》2014,102(5):437-447
We introduce a new class of unbounded model subdomains of \({\mathbb{C}^2}\) for the \({\Box_b}\) problem. Unlike previous finite type models, these domains need not be bounded by algebraic varieties. In this paper we obtain precise global estimates for the Carnot–Carathéodory metric induced on the boundary of such domains by the real and imaginary parts of the CR vector field. 相似文献
20.
E. Ekici 《Acta Mathematica Hungarica》2007,117(4):325-333
The main purpose of this paper is to introduce the concepts of *-sets, *-continuous functions and to obtain new decompositions of continuous and ηζ-continuous functions. Moreover, properties of *-sets and some properties of -sets are discussed.
相似文献