共查询到20条相似文献,搜索用时 0 毫秒
1.
Artur MichalakMarek Nawrocki 《Indagationes Mathematicae》2002,13(2):185-195
In the paper we describe the Banach envelopes of Hardy spaces of analytic functions of several variables on polydiscs taking values in quasi-Banach spaces. 相似文献
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H. O. Fattorini 《Applied Mathematics and Optimization》1974,1(2):163-188
We show here that a variant of Pontryagin's maximum principle holds for time-optimal trajectories of the systemu′ = Au + f that begin and end at the domain ofA. HereA is the infinitesimal generator of a strongly continuous semigroupS(·) in the reflexive Banach spaceE. This partly generalizes a result of Balakrishnan ([1]) where no conditions are assumed on the trajectories but whereS(t) is supposed to beonto for allt ≥ 0. A weakened version of the maximum principle is then proved forall time-optimal trajectories whenA generates an analytic semigroup andE is a Hilbert space. Finally, the results are modified to handle two examples involving the heat equation where the spaceE is not reflexive. 相似文献
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Per Enflo 《Acta Mathematica》1987,158(1):213-313
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With “hat” denoting the Banach envelope (of a quasi-Banach space) we prove that
if 0<p<1, 0<q<1, ℝ, while
if 0<p<1, 1≤q<+∞, ∝, and
if 1≤p<+∞, 0<q<1, ℝ.
Applications to questions regarding the global interior regularity of solutions to Poisson type problems for the three-dimensional
Lamé system in Lipschitz domains are presented. 相似文献
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E. Medina Galego 《Archiv der Mathematik》2002,79(4):299-307
We investigate the geometry of the Banach spaces failing Schroeder-Bernstein Property (SBP). Initially we prove that every complex hereditarily indecomposable Banach space H is isomorphic to a complemented subspace of a Banach space S(H) that fails SBP in such a way that the only complemented hereditarily indecomposable subspaces of S(H) are those which are nearly isomorphic to H. Then we show that every Banach space having Mazur property is isomorphic to some complemented subspace of a Banach space which is not isomorphic to its square but isomorphic to its cube. Finally, we prove that if a Banach space X fails SBP then either it is not primary or the Grothendieck group K0(L(X)) of the algebra of operators on X is not trivial. 相似文献
9.
Tuomas Hytönen 《Journal of Functional Analysis》2008,254(3):675-726
Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces Lp(Rn;X) of X -valued functions on Rn. We characterize Kato's square root estimates and the H∞-functional calculus of L in terms of R-boundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative Lp space. To do so, we develop various vector-valued analogues of classical objects in Harmonic Analysis, including a maximal function for Bochner spaces. In the special case X=C, we get a new approach to the Lp theory of square roots of elliptic operators, as well as an Lp version of Carleson's inequality. 相似文献
10.
Krishnan Balachandran 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(12):4587-4593
In this paper we prove the existence of solutions of certain kinds of nonlinear fractional integrodifferential equations in Banach spaces. Further, Cauchy problems with nonlocal initial conditions are discussed for the aforementioned fractional integrodifferential equations. At the end, an example is presented. 相似文献
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The concept of quasidifferential operator in a scale of Banach spaces is formulated. A theorem of existence and uniqueness of a solution to the Cauchy problem for the equation with a nonlinear quasidifferential operator is proved. As an example of application of the theorem, the correctness of the nonlinear nonlocal problem of plane-parallel unsteady potential motion of a liquid with free boundary is proved. 相似文献
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Daniel Pellegrino Eduardo V. Teixeira 《Bulletin of the Brazilian Mathematical Society》2009,40(3):417-431
The main result of the paper shows that, for 1 < p < ∞ and 1 ≤ q < ∞, a linear operator T: ℓ
p
→ ℓ
q
attains its norm if, and only if, there exists a not weakly null maximizing sequence for T (counterexamples can be easily constructed when p = 1). For 1 < p ≠ q < ∞, as a consequence of the previous result we show that any not weakly null maximizing sequence for a norm attaining operator
T: ℓ
p
→ ℓ
q
has a norm-convergent subsequence (and this result is sharp in the sense that it is not valid if p = q). We also investigate lineability of the sets of norm-attaining and non-norm attaining operators. 相似文献
14.
M. V. Falaleev 《Differential Equations》2008,44(8):1157-1169
We study the solvability of a degenerate heat equation with closed linear operators B multiplying the time derivative and A multiplying the Laplace operator in the class of generalized functions in Banach spaces. Under various assumptions on the operator pencil λB-A (it can be Fredholm of index zero, Fredholm, spectrally bounded, sectorial, or radial), we construct the fundamental operator function for the differential operator Bδ′(t) × δ ( $ \bar x $ ) ? Aδ(t) × Δδ ( $ \bar x $ ) and use it for the closed-form construction of the desired generalized solution of the Cauchy problem for the equation in question. We single out uniqueness classes for these solutions and analyze the relationship between continuous and generalized solutions. 相似文献
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We consider the identification problem of two operators having different properties for the systems governed by nonlinear evolution equations. For the identification problem, we show the existence of optimal solutions and present necessary optimality conditions. We illustrate the approach on two examples. 相似文献
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Denny H. Leung 《Israel Journal of Mathematics》2001,121(1):247-264
The space WeakL
1 consists of all Lebesgue measurable functions on [0,1] such thatq(f)=supcλ{t:|f(t)|>c} c>0 is finite, where λ denotes Lebesgue measure. Let ρ be the gauge functional of the convex hull of the unit ball {f:q(f)≤1} of the quasi-normq, and letN be the null space of ρ. The normed envelope of WeakL
1, which we denote byW, is the space (WeakL
1/N, ρ). The Banach envelope of WeakL
1,
, is the completion ofW. We show that
is isometrically lattice isomorphic to a sublattice ofW. It is also shown that all rearrangement invariant Banach function spaces are isometrically lattice isomorphic to a sublattice
ofW. 相似文献
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Guotao Wang Lihong Zhang Guangxing Song 《Journal of Applied Mathematics and Computing》2011,37(1-2):559-574
In this paper, by using the cone theory and monotone iterative technique, we investigate the existence of extremal solutions and unique solution of the integral boundary value problem for a class of first-order impulsive integro-differential equations in a real Banach space. An explicit iterative scheme for the unique solution and an error estimate of the approximation sequence are also derived. 相似文献
19.
Guang Gui Ding 《数学学报(英文版)》2015,31(12):1872-1878
In this article, we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces. We obtain that under some condition the answer to this problem is affirmative. 相似文献
20.
This paper deals with a regularity assumption for the mathematical programming problem in Banach spaces. The attractive feature of our constraint qualification is the fact that it can be considered as a condition on the active part only of the constraint, and that it is preserved under small perturbations. Moreover, we show that our condition is almost equivalent to the existence of a non-empty and weakly compact set of Lagrange multipliers. The main step in the proof of our results is a generalization of the open mapping theorem.The early parts of this article result from fruitful correspondence with S. Kurcyusz, who died tragically in 1978. This paper is dedicated to his memory. 相似文献