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51.
B. P. Paneah 《Functional Analysis and Its Applications》2003,37(1):46-60
In this paper, some solvability problems for functional equations of the form
are studied. Here I is a finite closed interval in , F is an unknown continuous function,
and
are given continuous maps of I into itself, and
, and
are real-valued continuous functions on I. Such equations are of interest not only by themselves as an object of analysis, but they are also a necessary link in solving various problems in such diverse fields as integral and functional equations, measure theory, and boundary problems for hyperbolic differential equations. The major part of the proofs is based on the new results in the theory of dynamical systems generated by a noncommutative semigroup with two generators. 相似文献
52.
本文考虑了R^n 1空间中椭圆函数和准椭圆函数的一些性质,然后分别讨论了周期和准周期Riemann边值问题,给出了解的表达式和可解条件。 相似文献
53.
矩阵方程AXB=D的最小二乘Hermite解及其加权最佳逼近 总被引:1,自引:0,他引:1
本中,我们讨论了矩阵方程AXB=D的最小二乘Hermite解,通过运用广义奇异值分解(GSVD),获得了解的通式。此外,对于给定矩阵F,也得到了它的加权最佳逼近表达式。 相似文献
54.
§ 1 . IntroductionSingularperturbationofDirichletproblemsforellipticequationswerediscussedbysomeauthors[1 ] -[4] ,butmostofwhathavebeenconsideredareboundeddomain .InthispapertheauthorconsiderDirichletexteriorproblemsasfollow :εL1 [u]+L2 [u]=f(x ,u ,ε) ,x∈Rn -Ω , ( 1)u(x) =g(x ,ε) ,x∈ Ω ,( 2 )whereL1 issecondorderellipticoperator:L1 [u]=∑ni,j=1aij(x) 2 u xi xj+∑ni=1ai(x) u xi +a(x ,u) ,∑ni,j=1aijζiζj ≥δ0 >0 ,x∈Rn -Ω , ζ∈Rn ,ζ≠ 0 ,L2 isfirstorderdifferentialopera… 相似文献
55.
映入E(q,p)的复合算子 总被引:3,自引:0,他引:3
§ 1 . Introduction LetD ={z:|z| <1}betheunitdiskofcomplexplane,H(D)bethespaceofallana lysticfunctionsonD ,denoteLebesguemeasureonDbydm ,normalizedsothatm(D) =1.Fora ∈D ,σa(z) =a-z1- az istheMobiustransformationofDtoitselfandg(z,a) =log|1- aza-z|istheGreenfunctionofDwithsingularityata.Everyanalyticself mapφ :D →DoftheunitdiskinducesthroughcompositionalinearcompositionoperatorCφfromH(D)toitself.Itisawell knownconsequenceofLittlewood’ssubordinationprinciple( [1],[2 ])that… 相似文献
56.
Mathematical Notes - 相似文献
57.
On a Problem of Karpilovsky 总被引:5,自引:0,他引:5
Let G be a finite elementary group. Let n (G) denote the nth power of the augmentation ideal (G) of the integral group ring G. In this paper, we give an explicit basis of the quotient group Qn(G) = n(G)/n+1 (G) and compute the order of Qn (G).2000 Mathematics Subject Classification: 16S34, 20C05 相似文献
58.
H. Petersson 《Acta Mathematica Hungarica》2003,100(1-2):69-81
The PDE-preserving operators O on the space of nuclearly entire functions of bounded type HNb(E) on a Banach space E are characterized. An operator is PDE-preserving when it preserves homogenous solutions to homogeneous convolution equations.
We establish a one to one correspondence between O and a set Σ of sequences of entire functionals, i.e. exponential type functions. In this way, algebraic structures on Σ,
such as ring structures, can be carried over to O and vice versa. In particular, it follows that O is a non-commutative ring (algebra) with unity with respect to composition and the convolution operators form a commutative
subring (subalgebra). We discuss range and kernel properties, for the operators in O, and characterize the projectors (onto polynomial spaces) in O by determining the corresponding elements in Σ.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
59.
Varghese Mathai 《Geometriae Dedicata》2003,99(1):1-15
We outline a twisted analogue of the Mishchenko–Kasparov approach to prove the Novikov conjecture on the homotopy invariance of the higher signatures. Using our approach, we give a new and simple proof of the homotopy invariance of the higher signatures associated to all cohomology classes of the classifying space that belong to the subring of the cohomology ring of the classifying space that is generated by cohomology classes of degree less than or equal to 2, a result that was first established by Connes and Gromov and Moscovici using other methods. A key new ingredient is the construction of a tautological C*
r
(, )-bundle and connection, which can be used to construct a C*
r
(, )-index that lies in the Grothendieck group of C*
r
(, ), where is a multiplier on the discrete group corresponding to a degree 2 cohomology class. We also utilise a main result of Hilsum and Skandalis to establish our theorem. 相似文献
60.
We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C
1 transformation. 相似文献