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1.
D. R. Lebedev S. Z. Pakuliak S. M. Khoroshkin 《Theoretical and Mathematical Physics》1997,110(1):18-34
The representation theory of centrally extended Yangian doubles is investigated. The intertwining operators are constructed
for infinite dimensional representations of
, which are deformed analogs of the highest weight representations of the affine algebra
at level 1. We give bosonized expressions for the intertwining operators and verify that they generate an algebra isomorphic
to the Zamolodchikov-Faddeev algebra for the SU(2)-invariant Thirring model. From them, we compose L-operators by Miki’s method
and verify that they coincide with L-operators constructed from the universal R-matrix. The matrix elements of the product
of these operators are calculated explicitly and are shown to satisfy the quantum (deformed) Knizhnik-Zamolodchikov equation
associated with the universal R-matrix for
.
This paper was written at the request of the Editorial Board.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 1, pp. 25–45. January, 1997. 相似文献
2.
Di He HU Zheng Yan XIAO 《数学学报(英文版)》2007,23(1):41-56
There are two parts in this paper. In the first part we construct the Markov chain in random environment(MCRE), the skew product Markov chain and p-θ^→ chain from a random transition matrix and a two-dimensional probability distribution, and in the second part we prove that the invarianee principle for p-θ^→ chain, a more complex non-homogeneous Markov chain, is true under some reasonable conditions. This result is more powerful. 相似文献
3.
Dong Zhe 《Czechoslovak Mathematical Journal》2006,56(2):287-298
In this paper we investigate finite rank operators in the Jacobson radical
of Alg(
), where
are nests. Based on the concrete characterizations of rank one operators in Alg(
) and
, we obtain that each finite rank operator in
can be written as a finite sum of rank one operators in
and the weak closure of
equals Alg(
) if and only if at least one of
is continuous. 相似文献
4.
Ferenc Weisz 《Acta Mathematica Hungarica》2002,96(1-2):149-160
A general summability method of two-dimensional Fourier transforms is given with the help of an integrable function
. Under some conditions on
we show that the maximal operator of the Marcinkiewicz-
-means of a tempered distribution is bounded from
to
for all
and, consequently, is of weak type
, where
depends only on
. As a consequence we obtain a generalization for Fourier transforms of a summability result due to Marcinkievicz and Zhizhiashvili,
more exactly, the Marcinkiewicz-
-means of a function
converge a.e. to the function in question. Moreover, we prove that the Marcinkiewicz-
-means are uniformly bounded on the spaces
and so they converge in norm
. Some special cases of the Marcinkievicz-
-summation are considered, such as the Weierstrass, Picar, Bessel, Fejér, de la Vallée-Poussin, Rogosinski and Riesz summations.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
Yehoram Gordon 《Israel Journal of Mathematics》1981,39(1-2):141-144
LetX andY be Banach spaces. TFAE (1)X andY do not contain subspaces uniformly isomorphic to
(2) The local unconditional structure constant of the space of bounded operatorsL (X*k,Y
k) tends to infinity for every increasing sequence
and
of finite-dimensional subspaces ofX andY respectively. 相似文献
6.
Xiu Gui LIU 《数学学报(英文版)》2007,23(6):1025-1032
Abstract Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by (b0hn-h1bn-1)∈ ExtA^3,(p^n+p)q(Zp,Zp) in the Adams spectral sequence. At the same time, he proved that i.(hlhn) ∈ExtA^2,(p^n+P)q(H^*M, Zp) is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element ξn∈π(p^n+p)q-2M. In this paper, with Lin's results, we make use of the Adams spectral sequence and the May spectral sequence to detect a new nontrivial family of homotopy elements jj′j^-γsi^-i′ξn in the stable homotopy groups of spheres. The new one is of degree p^nq + sp^2q + spq + (s - 2)q + s - 6 and is represented up to a nonzero scalar by hlhnγ-s in the E2^s+2,*-term of the Adams spectral sequence, where p ≥ 7, q = 2(p - 1), n ≥ 4 and 3 ≤ s 〈 p. 相似文献
7.
Franco Favilli 《Annali dell'Universita di Ferrara》1980,26(1):61-68
Summary Let Ω⊂⊂C
n
be a pseudo-convex domain with smooth real-analytic boundarybΩ; the local regularity in
of the
is then strictly related not only with the subellipticity of such problem, but also with certain geometric conditions onbΩ: ifn=2 and α is a (0,1)-form, such relations are equivalences.
Lavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R. 相似文献
Riassunto Se Ω⊂⊂C n è un dominio pseudo-convesso con frontierabΩ definita da una funzione analitica reale e ?liscia?, la regolarità locale delle soluzioni in del αè in stretta relazione non solo con la subellitticità di tale problema ma anche con certe condizioni geometriche sulla struttura dibΩ: sen=2 ed α è una (0,1)-forma, tali relazioni sono delle equivalenze.
Lavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R. 相似文献
8.
We define the Hopf algebra structure on the Grothendieck group of finite-dimensional polynomial representations of
in the limitN→∞. The resulting Hopf algebra Rep
is a tensor product of its Hopf subalgebras Repa
,a ∈ ℂ×/q2ℤ. Whenq is generic (resp.,q
2 is a primitive root of unity of orderl), we construct an isomorphism between the Hopf algebra Rep
a
and the algebra of regular functions on the prounipotent proalgebraic group
(resp.,
). Whenq is a root of unity, this isomorphism identifies the Hopf subalgebra of Rep
a
spanned by the modules obtained by pullback with respect to the Frobenius homomorphism with the algebra generated by the
coefficients of the determinant of an element of
considered as anl×l matrix over the Taylor series. This gives us an explicit formula for the Frobenius pullbacks of the fundamental representations.
In addition, we construct a natural action of the Hall algebra associated to the infinite linear quiver (resp., the cyclic
quiver withl vertices) on Rep
a
and describe the span of tensor products of evaluation representations taken at fixed points as a module over this Hall algebra. 相似文献
9.
Let
denote the class of ergodic probability preserving transformations which are disjoint from every weakly mixing system. Let
be the class of multipliers for
, i.e. ergodic transformations whose all ergodic joinings with any element of
are also in
. Fix an ergodic rotationT, a mildly mixing actionS of a locally compact second countable groupG and an ergodic cocycle ϕ forT with values inG. The main result of the paper is a sufficient (and also necessary by [LeP] whenG is countable Abelian andS is Bernoullian) condition for the skew product build fromT, ϕ andS to be an element of
. Moreover, the self-joinings of such extensions ofT are described with an application to study semisimple extensions of rotations.
Dedicated to Hillel Furstenberg on the occasion of his retirement
The first-named author was supported in part by CRDF, grant UM1-2546-KH-03.
The second-named author was supported in part by KBN grant 1P03A 03826. 相似文献
10.
We prove that many subgroups of free profinite groups are free, and use this to give new examples of pseudo-algebraically
closed subfields of
satisfying Hilbert’s Irreducibility Theorem, and to solve problems posed by M. Jarden and A. Macintyre. We also find a subfield
of
which does not satisfy Hilbert’s Irreducibility Theorem, but all of whose proper finite extensions do.
The first author was supported by NSF grant MCS76-11625. 相似文献
11.
A. I. Zenchuk 《Theoretical and Mathematical Physics》1999,119(1):431-437
A new method is suggested for constructing Miura-type transformations for systems of nonlinear equations of mathematical physics
integrable by the
-problem method using a generalized normalization function in the
-problem. Examples of these transformations for the Kadomtsev-Petviashvili equation are considered.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 1, pp. 47–54, April, 1999. 相似文献
12.
A. S. Fedorenko 《Ukrainian Mathematical Journal》2000,52(6):981-986
We consider the approximation of functions of the classes of
by Zygmund sums. In papticular, we present asymptotic equalities for the quantities
under various conditions imposed on functions ψ1(·) and ψ2(·).
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52,
No. 6, pp. 856–860, June, 2000. 相似文献
13.
Mats Andersson 《Journal d'Analyse Mathématique》1996,68(1):39-58
LetG
1,…,Gm be bounded holomorphic functions in a strictly pseudoconvex domainD such that
. We prove that for each
(0,q)-form ϕ inL
p(∂D), 1<p<∞, there are
formsu
1, …,u
m inL
p(∂D) such that ΣG
juj=ϕ. This generalizes previous results forq=0. The proof consists in delicate estimates of integral representation formulas of solutions and relies on a certainT1 theorem due to Christ and Journé. For (0,n−1)-forms there is a simpler proof that also gives the result forp=∞. Restricted to one variable this is precisely the corona theorem.
The author was partially supported by the Swedish Natural Research Council. 相似文献
14.
A necessary and sufficient condition for regularity of the
-Neumann operator on (0,q)-forms in a smooth bounded pseudoconvex domain in Cn is that the orthogonal projections onto
-closed forms of degrees (0,q−1), (0,q), and (0,q+1) all be regular.
The first author partially supported by NSF Grant DMS-8701038 相似文献
15.
Ivan Č. Jovanović Eberhard Malkowsky Vladimir Rakočević 《Rendiconti del Circolo Matematico di Palermo》2003,52(2):308-314
LetF be aBK space withAK and
denote the set of all formal power series
with
such that
ε F for the sequence of coefficients of
. We give a necessary and sufficient condition for a point to be a bounded point evaluation on
, and for a polynomial to be cyclic in
. As special cases, we obtain the results for the space ℓ
p
(β) in [7].
Research of the authors supported under the research project #1232 of the Serbian Ministry of Sciences and Tecnology and,
in the case of the second author, also by the DAAD foundation (German Academic Exchange Service), grant 911 103 102 8. 相似文献
16.
G. E. Arutyunov L. O. Chekhov S. A. Frolov 《Theoretical and Mathematical Physics》1997,111(2):536-562
It is shown that the classical L-operator algebra of the elliptic Ruijsenaars-Schneider model can be realized as a subalgebra
of the algebra of functions on the cotangent bundle over the centrally extended current group in two dimensions. It is governed
by two dynamic τ and
-matrices satisfying a closed system of equations. The corresponding quantum R- and
-matrices are found as solutions to quantum analogues of these equations. We present the quantum L-operator algebra and show
that the system of equations for R and
arises as the compatibility condition for this algebra. It turns out that the R-matrix is twist-equivalent to the Felder
elliptic RF-matrix, with
playing the role of the twist. The simplest representation of the quantum L-operator algebra corresponding to the elliptic
Ruijsenaars-Schneider model is obtained. The connection of the quantum L-operator algebra to the fundamental relation RB LL=LLRB with the Belavin elliptic R-matrix is established. As a by-product of our construction, we find a new N-parameter elliptic
solution to the classical Yang-Baxter equation.
This paper was written at the request of the Editorial Board.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 2, pp. 182–217, May, 1997. 相似文献
17.
A. M. Gainutdinov A. M. Semikhatov I. Yu. Tipunin B. L. Feigin 《Theoretical and Mathematical Physics》2006,148(3):1210-1235
To study the representation category of the triplet W-algebra
that is the symmetry of the (1, p) logarithmic conformal field theory model, we propose the equivalent category C
p
of finite-dimensional representations of the restricted quantum group Ū
q
sℓ(2) at
. We fully describe the category C
p
by classifying all indecomposable representations. These are exhausted by projective modules and three series of representations
that are essentially described by indecomposable representations of the Kronecker quiver. The equivalence of the
-and Ū
q
sℓ(2)-representation categories is conjectured for all p = 2 and proved for p = 2. The implications include identifying the
quantum group center with the logarithmic conformal field theory center and the universal R-matrix with the braiding matrix.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 3, pp. 398–427, September, 2006. 相似文献
18.
The classical factorization method reduces the study of a system of ordinary differential equations Ut=[U+, U] to solving algebraic equations. Here U(t) belongs to a Lie algebra
which is the direct sum of its subalgebras
and
, where “+” signifies the projection on
. We generalize this method to the case
. The corresponding quadratic systems are reducible to a linear system with variable coefficients. It is shown that the generalized
version of the factorization method can also be applied to Liouville equation-type systems of partial differential equations.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 3, pp. 339–350, March, 1997. 相似文献
19.
It is proved that an irreducible quasifinite
-module is a highest or lowest weight module or a module of the intermediate series; a uniformly bounded indecomposable weight
-module is a module of the intermediate series. For a nondegenerate additive subgroup Λ ofF
n, whereF is a field of characteristic zero, there is a simple Lie or associative algebraW(Λ,n)(1) spanned by differential operatorsuD
1
m
…D
1
m
foru ∈F[Γ] (the group algebra), andm
i≥0 with
, whereD
i are degree operators. It is also proved that an indecomposable quasifinite weightW(Λ,n)(1)-module is a module of the intermediate series if Λ is not isomorphic to ℤ.
Supported by NSF grant no. 10471091 of China and two grants “Excellent Young Teacher Program” and “Trans-Century Training
Programme Foundation for the Talents” from the Ministry of Education of China. 相似文献
20.
Hengwu Zheng 《Semigroup Forum》1995,51(1):217-223
In this paper we describe the strong
-congruences on
-regular semigroups in terms of their characteristic kernels and characteristic traces.
This paper formed a part of the author's doctoral dissertation, written under the direction of Professor Yuqi Guo at Lanzhou
University. The author wishes to give many thanks to the supervisor for his encouragement and help. 相似文献