共查询到20条相似文献,搜索用时 94 毫秒
1.
本文给出一类型如P(x,D)=D14+x14D24-(i1/2+(-i)1/2)D12D2+4x1D1D22-i(i1/2-(-i)1/2)x12D23+(1+2i)D22+C 或更一般地p(x,D)=LtL(x,D)+C(L为无解算子)的多重特征算子。指出包括零阶项在内的低阶项对局部可解性能具有决定性影响。具体地说,在原点邻域上面所给算子p(x,D)的主部D14+x14D24为可解算子,当C=0时P(x,D)为不可解算子。但当C>0时又变为局部可解算子。类似地讨论了算子附加零阶项的一些情况。文章最后证明了当自由项f具形|x1|ψ'(x2)(ψ为实函数)时,在原点邻域有古典解的充要条件为ψ(x2)解析。 相似文献
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李玉成 《数学物理学报(A辑)》2000,20(2):235-239
该文考虑方程组
t(ux - vy - wt ) + w = 0 (H)
uy = -vx, ut = -wx, vt = wy
的解f = u + iv + jt ∈C2,找到(H)可解的一个充要条件,并讨论相关边值问题解的存在性和积分表示,推广了1992年H. Leutwiler[1]的结果. 相似文献
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设un为n阶酉群。u∈L1(Un)的Fourier级数的第二型Cesáro平均为σNα(u,U)=KN*αu(U),其中 KNα(U)=sum from (N≥li>…>ln≥-N)(Al1α…A1uN(f)Xf(U)),U∈Un为相应的核函数。本文给出“Lebesgue常数”‖KNα‖(L1(Un))的精确估计,并由此建立了酉群上函数的Fourier级数按第二型Cesáro求和收敛于自身的条件。 相似文献
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本文在m+1连通区域上研究方程(A)wg=g(z,w,wz),(A.1)|g(z,w,wz1)-(z,w,wz2)|≤q0|wz1-wz2|,q0=常数<1 (A.2)的Riemann和Hilbert复合边值问题(RH问题)。我们构造了算子θ(w,z),研究了其连续与微分性质,建立了解的表示定理、先验估计、存在唯一性定理(K≥m)与可解条件(K≤m-1)。 相似文献
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本文首先在一般的赋范线性空间中研究了集值映射F;X→Y的平衡点的存在性问题,证明了包含问题O∈F(X)的三个可解性定理.然后在无穷维空间中研究了弱相依锥Tkσ(x)的直接像,弱相依导数DσF(x,y)的一个链式法则以及偏y弱导数DyσF(x,y)的弱Lip连续性.最后,作为应用,给出并证明了用弱相依导数DσF(x,y)及弱P导数PσF(x,y)判定无穷维 相似文献
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本文讨论了四元数分析中多圆柱区域上方程∂znu(z) = f 的Dirichlet 边值问题. 获得问题的可解条件, 并当可解条件满足时, 给出了解的积分表示. 相似文献
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V. G. Bardakov 《Acta Appl Math》2005,85(1-3):41-48
In this paper we prove that the braid group Bn(S2) of 2-sphere, mapping class group M(0,n) of the n-punctured 2-sphere and the braid group B3(P2) of the projective plane are linear.
Partially supported by the Russian Foundation for Basic Research (grant number 02-01-01118).Mathematics Subject Classifications (2000) 20F28, 20F36, 20G35. 相似文献
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O. V. Shvartsman 《Functional Analysis and Its Applications》2009,43(2):132-139
Let Γ ? U (1, 1) be the subgroup generated by the complex reflections. Suppose that Γ acts discretely on the domain K = {(z 1, z 2) ∈ ?2 ||z 1|2 ? |z 2|2 < 0} and that the projective group PΓ acts on the unit disk B = {|z 1/z 2| < 1} as a Fuchsian group of signature (n 1, ..., n s ), s ? 3, n i ? 2. For such groups, we prove a Chevalley type theorem, i.e., find a necessary and sufficient condition for the quotient space K/Γ to be isomorphic to ?2 ? {0}. 相似文献
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It is proved that finite simple groups L4(2m), m ⩾ 2, and U4(2m), m ⩾ 2, are, up to isomorphism, recognized by spectra, i.e., sets of their element orders, in the class of finite groups.
As a consequence the question on recognizability by spectrum is settled for all finite simple groups without elements of order
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Supported by RFBR (grant Nos. 05-01-00797 and 06-01-39001), by SB RAS (Complex Integration project No. 1.2), and by the Ministry
of Education of China (Project for Retaining Foreign Expert).
Supported by NSF of Chongqing (CSTC: 2005BB8096).
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Translated from Algebra i Logika, Vol. 47, No. 1, pp. 83–93, January–February, 2008. 相似文献
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In Sook Park 《Mathematische Nachrichten》2008,281(4):561-574
It is shown that for any locally compact abelian group ?? and 1 ≤ p ≤ 2, the Fourier type p norm with respect to ?? of a bounded linear operator T between Banach spaces, denoted by ‖T |?????p‖, satisfies ‖T |?????p‖ ≤ ‖T |?????p‖, where ?? is the direct product of ?2, ?3, ?4, … It is also shown that if ?? is not of bounded order then Cnp ‖T |?????p‖ ≤ ‖T |?????p‖, where ?? is the circle group, n is a onnegative integer and Cp = . From these inequalities, for any locally compact abelian group ?? ‖T |?????2‖ ≤ ‖T |?????2‖, and moreover if ?? is not of bounded order then ‖T |?????2‖ = ‖T |?????2‖. The Hilbertian property and B‐convexity are discussed in the framework of Fourier type p norms. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Let 𝒲 be the Virasoro-like algebra, and d 1, d 2 be the degree derivations of 𝒲. Set ? = W⊕C d 1⊕C d 2. Let F α(V) be the ?-module defined by Larsson's functor applied to a finite dimensional sl 2-module V. In this article, the derivations from ? to ?-modules F α(V) and the first cohomology group H 1(?, F α(V)) are given. 相似文献
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We have described the structure of Q n (G) = Δ n (G)/Δ n+1(G) for 35 particular classes of groups G with order 25 in the previous article. In this article, the structure of Q n (G) for all the remaining classes of groups G with order 25 are presented. 相似文献
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Let U = ℂ2, Γ = ℤ2, and let ℂ[x
1±1, x
2±1] be the ring of Laurent polynomials. The Witt algebra L is the Lie algebra of derivations over ℂ[x
1±1, x
2±1], which is spanned by elements of the form D(u, r) = x
r
(u
1
d
1 + u
2
d
2), u = (u
1, u
2) ∈ U, r ∈ Γ, where d
1 and d
2 are the degree derivations of ℂ[x
1±1, x
2±1]. The image of gl
2-module V under Larsson functor F
α
, denoted by W = F
α
(V), gives a class of L-modules, often called the Larsson-modules of L. In this paper, we study the derivations from the Witt algebra L to its Larsson-modules W, and we determine the first cohomology group H
1(L,W). 相似文献
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Let {ie166-01} be a set of finite groups. A group G is said to be saturated by the groups in {ie166-02} if every finite subgroup
of G is contained in a subgroup isomorphic to a member of {ie166-03}. It is proved that a periodic group G saturated by groups
in a set {U3(2m) | m = 1, 2, …} is isomorphic to U3(Q) for some locally finite field Q of characteristic 2; in particular, G is locally finite.
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Translated from Algebra i Logika, Vol. 47, No. 3, pp. 288–306, May–June, 2008. 相似文献
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We present the construction for a u-product G1 ○ G2 of two u-groups G1 and G2, and prove that G1 ○ G2 is also a u-group and that every u-group, which contains G1 and G2 as subgroups and is generated by these, is a homomorphic image of G1 ○ G2. It is stated that if G is a u-group then the coordinate group of an affine space Gn is equal to G ○ Fn, where Fn is a free metabelian group of rank n. Irreducible algebraic sets in G are treated for the case where G is a free metabelian
group or wreath product of two free Abelian groups of finite ranks.
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Translated from Algebra i Logika, Vol. 44, No. 5, pp. 601–621, September–October, 2005.
Supported by RFBR grant No. 05-01-00292, by FP “Universities of Russia” grant No. 04.01.053, and by RF Ministry of Education
grant No. E00-1.0-12. 相似文献