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921.
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
922.
This paper is concerned with the Poincaré-Steklov operator that is widely used in domain decomposition methods. It is proved that the inverse of the Poincaré-Steklov operator can be expressed explicitly by an integral operator with a kernel being the Green's function restricted to the interface. As an application, for the discrete Poincaré-Steklov operator with respect to either a line (edge) or a star-shaped web associated with a single vertex point, a preconditioner can be constructed by first imbedding the line as the diameter of a disk, or the web as a union of radii of a disk, and then using the Green's function on the disk. The proposed technique can be effectively used in conjunction with various existing domain decomposition techniques, especially with the methods based on vertex spaces (from multi-subdomain decomposition). Some numerical results are reported.
923.
The capacitance matrix method has been implemented in a primitive equation ocean model to accommodate islands and portions of irregular coastal boundaries that cannot be treated adequately by boundary-fitted orthogonal curvilinear co-ordinates. The algorithm preserves the ability to solve the streamfunction equation using fast and accurate elliptic solvers that require a rectangular computational domain. By superposition of a set of island Green functions, the solution is adjusted to ensure continuity of pressure around each island. The implementation is tested by comparison with an analytic solution for wind-driven flow in a closed basin similar to the southwest Pacific Ocean. 相似文献
924.
Xiao-Chuan Cai William D. Gropp David E. Keyes 《Numerical Linear Algebra with Applications》1994,1(5):477-504
In recent years, competitive domain-decomposed preconditioned iterative techniques of Krylov-Schwarz type have been developed for nonsymmetric linear elliptic systems. Such systems arise when convection-diffusion-reaction problems from computational fluid dynamics or heat and mass transfer are linearized for iterative solution. Through domain decomposition, a large problem is divided into many smaller problems whose requirements for coordination can be controlled to allow effective solution on parallel machines. A central question is how to choose these small problems and how to arrange the order of their solution. Different specifications of decomposition and solution order lead to a plethora of algorithms possessing complementary advantages and disadvantages. In this report we compare several methods, including the additive Schwarz algorithm, the classical multiplicative Schwarz algorithm, an accelerated multiplicative Schwarz algorithm, the tile algorithm, the CGK algorithm, the CSPD algorithm, and also the popular global ILU-family of preconditioners, on some nonsymmetric or indefinite elliptic model problems discretized by finite difference methods. The preconditioned problems are solved by the unrestarted GMRES method. A version of the accelerated multiplicative Schwarz method is a consistently good performer. 相似文献
925.
Marius Ghergu 《Journal of Mathematical Analysis and Applications》2007,333(1):265-273
We are concerned with singular elliptic equations of the form −Δu=p(x)(g(u)+f(u)+a|∇u|) in RN (N?3), where p is a positive weight and 0<a<1. Under the hypothesis that f is a nondecreasing function with sublinear growth and g is decreasing and unbounded around the origin, we establish the existence of a ground state solution vanishing at infinity. Our arguments rely essentially on the maximum principle. 相似文献
926.
Chao Liu Lin Huang Dexing Feng 《Journal of Mathematical Analysis and Applications》2007,331(1):655-668
In this paper, a class of pendulum-like systems in infinite-dimensional Hilbert spaces is investigated. A frequency domain criterion guaranteeing the systems with the property of Lagrange stability is established. 相似文献
927.
V. P. Spiridonov 《Theoretical and Mathematical Physics》2007,150(2):266-277
We consider an elliptic analogue of the Gauss hypergeometric function and two of its multivariate generalizations. We describe
their relation to elliptic beta integrals, the exceptional Weyl group E7, the elliptic hypergeometric equation, and Calogero-Sutherland-type models.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 311–324, February, 2007. 相似文献
928.
È. M. Saydamatov 《Siberian Advances in Mathematics》2007,17(3):213-226
In the article we study the questions of well-posedness of general nonlocal boundary value problems for pseudodifferential equations in the Besov-type limit spaces. 相似文献
929.
姚景齐 《应用泛函分析学报》2002,4(1):93-96
A是Banach空间X中余弦算子函数C(t),t∈R,和正弦算子函数S(t),t∈R,的生成元。本证明了,对每个f∈C([0,T];X),连续函数u,u(t)=∫-tS(t-s)f(s)ds,f∈[0,T]是二阶非齐次0初值问题,u″=Au f的强解的充要条件是:A是空间X中的有界算子。 相似文献
930.
V. S. Pilidi 《Mathematical Notes》1997,62(3):360-367
A criterion is obtained for the applicability of the approximation method based on strongly approximating operator families
converging to a one-dimensional singular integral operator with coefficients continuous in the circle. Some special cases
are considered.
Translated fromMatematischeskie Zametki, Vol. 62, No. 3, pp. 430–439, September, 1997.
Translated by A. M. Chebotarev 相似文献