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81.
O. I. Reinov 《Journal of Mathematical Sciences》2003,115(2):2243-2250
We investigate Banach spaces possessing (or not possessing) the approximation properties AP s, 0 < s ≤ 1, in connection with the following known question in the geometric theory of operators: under which conditions on Banach spaces X and Y and on positive numbers r and p does the p-nuclearity of the second adjoint of a continuous operator T from X to Y imply the p-nuclearity of T? Actually, we give necessary and sufficient conditions under which this question is answered affirmatively. In addition, the corresponding counterexamples are obtained in the maximally strong form. For instance, it is shown (and this statement is a significant strengthening of the previous results of that sort) that there exists a pair of separable Banach spaces Z and W such that the spaces Z ** and W have Schauder bases, while for every p, 1 ≤ p < 2, there is a non-p-nuclear operator from W to Z with a p-nuclear second adjoint. Earlier, in similar examples, the corresponding spaces did not possess even the Grothendieck approximation property. The technique developed in this paper does not allow us to treat the case p > 2. That case will be studied in a forthcoming paper of the author. Bibliography: 11 titles. 相似文献
82.
For an arbitrary finite time interval, the unique solvability of a linear half-space problem is obtained in Hölder classes of functions. The problem arises as the result of the linearization of a free boundary problem for the Navier--Stokes system governing the unsteady motion of a finite mass of a compressible fluid. The boundary conditions in the linear problem are noncoercive because of the surface tension acting on the free boundary. This fact presents the main difficulty in the problem, while the differential system in itself is parabolic in the sense of Petrovskii. The principal idea of the investigation is to reduce the noncoercive problem to a coercive one with zero coefficient of the surface tension. Bibliography: 6 titles. 相似文献
83.
We prove new theorems on the justification of the averaging method for multifrequency oscillation systems with pulse influence at fixed times. 相似文献
84.
We consider the inverse problem of finding the unknown time-dependent leading coefficient and the free term in a parabolic equation. Boundary conditions and overdetermination conditions are local. We find conditions for the uniqueness and local existence. 相似文献
85.
86.
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88.
We prove that the sufficient conditions for the asymptotic stability of impulsive systems obtained by Gurgula and Perestyuk are also necessary conditions. 相似文献
89.
Ya. I. Diasamidze 《Journal of Mathematical Sciences》2003,117(4):4271-4319
90.