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An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with a potential function for the optimization problems with inequality constraints. The favorable properties of both the Löwner operator and the corresponding augmented Lagrangian are discussed. And under some mild assumptions, the rate of convergence of the augmented Lagrange algorithm is studied in detail. 相似文献
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Let(Φ, Ψ) be a pair of complementary N-functions and HΦ(A) and HΨ(A) be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg and innerouter type factorization theorems of Hp(A) to this case. 相似文献
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Steven R. Bell 《Advances in Mathematics》2002,172(1):15-52
We show that the classical kernel and domain functions associated to an n-connected domain in the plane are all given by rational combinations of three or fewer holomorphic functions of one complex variable. We characterize those domains for which the classical functions are given by rational combinations of only two or fewer functions of one complex variable. Such domains turn out to have the property that their classical domain functions all extend to be meromorphic functions on a compact Riemann surface, and this condition will be shown to be equivalent to the condition that an Ahlfors map and its derivative are algebraically dependent. We also show how many of these results can be generalized to finite Riemann surfaces. 相似文献
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L. E. Labuschagne 《Proceedings of the American Mathematical Society》2005,133(12):3643-3646
For almost forty years now the most frustrating open problem regarding the theory of finite maximal subdiagonal algebras has been the question regarding the universal validity of a non-commutative Szegö theorem and Jensen inequality (Arveson, 1967). These two properties are known to be equivalent. Despite extensive efforts by many authors, their validity has to date only been established in some very special cases. In the present note we solve the general problem in the affirmative by proving the universal validity of Szegö's theorem for finite maximal subdiagonal algebras.
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Saburou Saitoh 《Proceedings of the American Mathematical Society》1997,125(12):3633-3639
Let be an arbitrary map from an abstract set into an abstract set . We shall use the theory of reproducing kernels to provide a general method for representing the inverse map in terms of . We give several concrete examples of this method.
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We obtain the Laurent polynomial of Hermite interpolation on the unit circle for nodal systems more general than those formed by the n-roots of complex numbers with modulus one. Under suitable assumptions for the nodal system, that is, when it is constituted by the zeros of para-orthogonal polynomials with respect to appropriate measures or when it satisfies certain properties, we prove the convergence of the polynomial of Hermite-Fejér interpolation for continuous functions. Moreover, we also study the general Hermite interpolation problem on the unit circle and we obtain a sufficient condition on the interpolation conditions for the derivatives, in order to have uniform convergence for continuous functions.Finally, we obtain some improvements on the Hermite interpolation problems on the interval and for the Hermite trigonometric interpolation. 相似文献
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Vanessa Bertoni 《Journal of Mathematical Analysis and Applications》2007,332(1):418-427
Two sequences of polynomials are studied. One satisfies a three term recurrence relation for specific parameters and another a para-orthogonality property. Using the fact that these polynomials have their zeros lying on the unit circle and some other properties, we establish a criterion in order that the polynomials be univalent in the open unit disk. 相似文献
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Mourad E. H. Ismail Mizan Rahman 《Proceedings of the American Mathematical Society》1996,124(7):2149-2159
We find the raising and lowering operators for orthogonal polynomials on the unit circle introduced by Szego and for their four parameter generalization to biorthogonal rational functions on the unit circle.
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We exhibit examples of almost periodic Verblunsky coefficients for which Herman’s subharmonicity argument applies and yields the result that the associated Lyapunov exponents are uniformly bounded away from zero. As an immediate consequence of this result, we obtain examples of almost periodic Verblunsky coefficients for which the associated probability measure on the unit circle is pure point. 相似文献