共查询到20条相似文献,搜索用时 15 毫秒
1.
G. Molteni 《Acta Mathematica Hungarica》2007,117(1-2):61-76
Let ζ be a primitive q′-root of unity. We prove that the series $ \sum\nolimits_{n = 1}^\infty {{{\zeta ^{ \llcorner n\theta \lrcorner } } \mathord{\left/ {\vphantom {{\zeta ^{ \llcorner n\theta \lrcorner } } n}} \right. \kern-0em} n}} $ for θ ∈ Q converges if and only if θ = p/q with (p,q) = 1 and q′ ? p, and that there exists an uncountable set S of Liouville’s numbers such that the series does not converge when θ ∈ S. 相似文献
2.
In this paper we determine the method of multi-parameter interpolation and the scales of Lebesgue spaces $B_{\vec p} \left[ {0,2\pi } \right)$ and Besov spaces $B_{\vec p}^{\vec \alpha } \left[ {0,2\pi } \right)$ , which are generalizations of the Lorentz spacesL pq [0, 2π) and Besov spacesB pq α [0, 2π). We also prove imbedding theorems. 相似文献
3.
Patrick J. Rabier 《Mathematische Zeitschrift》2012,270(1-2):369-393
We give a fairly complete exposition of the Fredholm properties of the Douglis–Nirenberg elliptic systems on ${\mathbb{R}^{N}}$ in the classical (unweighted) L p Sobolev spaces and under “minimal” assumptions about the coefficients. These assumptions rule out the use of classical pseudodifferential operator theory, although it is indirectly of assistance in places. After generalizing a necessary and sufficient condition for Fredholmness, already known in special cases, various invariance properties are established (index, null space, etc.), with respect to p and the Douglis–Nirenberg numbers. Among other things, this requires getting around the problem that the L p spaces are not ordered by inclusion. In turn, with some work, invariance leads to a regularity theory more general than what can be obtained by the method of differential quotients. 相似文献
4.
Guram Donadze 《Proceedings Mathematical Sciences》2018,128(1):6
In [1], Anderson and Badawi conjectured that \(\mathrm{rad}(I)^n \subseteq I\) for every n-absorbing ideal I of a commutative ring. In this article, we prove their conjecture. We also prove related conjectures for radical ideals. 相似文献
5.
We obtain, among others, an exact estimate of the deviation of the “hyperbolic” Fourier-Hermite sums of the functions in the class L 2 r (D) of the space indicated in the title. 相似文献
6.
M. I. Graev 《Acta Appl Math》2004,81(1):93-120
Complex analogs of the Gelfand–Tsetlin patterns are introduced. Infinite-dimensional representations of $\mathfrak{g}\mathfrak{l}\left( {n,\mathbb{C}} \right)$ in the vector spaces spanned on these patterns are constructed. Exponentials of these representations are described. These exponentials are operators T(x), x∈GL(n,C), defined only in neighborhoods of the identity element of GL(n,C). A system of differential-difference equations for matrix elements of operators T(x) is constructed. Explicit formulas for matrix elements are obtained for the case x∈Z ±, where Z + and Z ? are the triangular unipotent subgroups. Representations of $\mathfrak{g}\mathfrak{l}\left( {n,\mathbb{C}} \right)$ are also constructed; bases of these representations consist of Gelfand–Tsetlin patterns having infinitely many rows. 相似文献
7.
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
8.
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
9.
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
10.
Roland Schmidt 《Archiv der Mathematik》2011,96(1):31-37
Let ${2\leq k\in \mathbb{N}}$ . Recently, Costantini and Zacher obtained a lattice-theoretic characterization of the classes ${\mathfrak{N}^k}$ of finite soluble groups with nilpotent length at most k. It is the aim of this paper to give a lattice-theoretic characterization of the classes ${\mathfrak{N}^{k-1}\mathfrak{A}}$ of finite groups with commutator subgroup in ${\mathfrak{N}^{k-1}}$ ; in addition, our method also yields a new characterization of the classes ${\mathfrak{N}^k}$ . The main idea of our approach is to use two well-known theorems of Gaschütz on the Frattini and Fitting subgroups of finite groups. 相似文献
11.
We describe along the guidelines of Kohn (Quantitative Estimates for Global Regularity. Analysis and Geometry in Several Complex Variables, pp. 97–128. Trend Math. Birkhäuser, Boston, 1999), the constant ${\mathcal {E}}_s$ which is needed to control the commutator of a totally real vector field $T_{{\mathcal {E}}}$ with $\bar{\partial }^*$ in order to have $H^s$ a-priori estimates for the Bergman projection $B_k, k\ge q-1$ , on a smooth $q$ -convex domain $D\subset \subset {\mathbb {C}}^{n}$ . This statement, not explicit in Kohn (Quantitative Estimates for Global Regularity. Analysis and Geometry in Several Complex Variables, pp. 97–128. Trend Math. Birkhäuser, Boston, 1999), yields regularity of $B_k$ in specific Sobolev degree $s$ . Next, we refine the pseudodifferential calculus at the boundary in order to relate, for a defining function $r$ of $D$ , the operators $(T^+)^{-\frac{\delta }{2}}$ and $(-r)^{\frac{\delta }{2}}$ . We are thus able to extend to general degree $k\ge 0$ of $B_k$ , the conclusion of (Quantitative Estimates for Global Regularity. Analysis and Geometry in Several Complex Variables, pp. 97–128. Trend Math. Birkhäuser, Boston, 1999) which only holds for $q=1$ and $k=0$ : if for the Diederich–Fornaess index $\delta $ of $D$ , we have $(1-\delta )^{\frac{1}{2}}\le {\mathcal {E}}_s$ , then $B_k$ is $H^s$ -regular. 相似文献
12.
Bo Chen 《Algebras and Representation Theory》2012,15(5):901-920
Let Q be a tame quiver of type $\widetilde{\mathbb{A}}_n$ and Rep(Q) the category of finite dimensional representations over an algebraically closed field. A representation is simply called a module. It will be shown that a regular string module has, up to isomorphism, at most two Gabriel–Roiter submodules. The quivers Q with sink-source orientations will be characterized as those, whose central parts do not contain preinjective modules. It will also be shown that there are only finitely many (central) Gabriel–Roiter measures admitting no direct predecessors. This fact will be generalized for all tame quivers. 相似文献
13.
Ukrainian Mathematical Journal - Over an arbitrary ring, a module M is said to be $$ {\mathcal{Z}}^{\ast } $$-semilocal if every submodule U of M has a $$ {\mathcal{Z}}^{\ast } $$ -supplement V in... 相似文献
14.
A combinatorial proof that the number of points of the space \(\overline {{M_{0,n}}} \left( {{F_q}} \right)\) satisfies the recurrent formula for the Poincaré polynomials of the space \(\overline {{M_{0,n}}} \left( \mathbb{C} \right)\) is obtained. 相似文献
15.
Theodor Wulf 《Monatshefte für Mathematik》1897,8(1):43-53
16.
17.
Ukrainian Mathematical Journal - We establish the exact-order estimates for the approximation of the classes $$ {S}_{1,\theta}^rB\left({\mathrm{\mathbb{R}}}^d\right) $$ by entire functions of... 相似文献
18.
M. V. Buslaeva 《Journal of Mathematical Sciences》1983,22(1):1032-1035
The asymptotic behavior asn, m → ∞ of the sum $$\sum\limits_{\kappa ,\ell = m}^{n - 1} {\exp \left[ {i\omega \sqrt n \left( {\sqrt \kappa + \sqrt \ell } \right)} \right]} \Phi \left( {1 - \frac{{\left| {\sqrt \kappa - \sqrt \ell } \right|}}{\Delta }} \right)$$ is studied where π(t)=0 for t?0 and φ(t)=t for t > 0. 相似文献
19.
Luigi Merli 《Annali di Matematica Pura ed Applicata》1958,46(1):97-107
20.
The criterion for the denseness of polynomials in the space
established by Hamburger in 1921 is extended to the spaces
, 1 p < . 相似文献