| 1. |
- Astashkin, Sergey V., et al.
(författare)
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Multiplicator space and complemented subspaces of rearrangement invariant space
- 2003
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Ingår i: Journal of Functional Analysis. - 0022-1236 .- 1096-0783. ; 202:1, s. 247-276
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Tidskriftsartikel (refereegranskat)abstract
- We show that the multiplicator space M(X) of an rearrangement invariant (r.i.) space X on [0, 1] and the nice part N0 (X) of X, that is, the set of all a ∈ X for which the subspaces generated by sequences of dilations and translations of a are uniformly complemented, coincide when the space X is separable. In the general case, the nice part is larger than the multiplicator space. Several examples of descriptions of M(X) and N0(X) for concrete X are presented
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| 2. |
- Borichev, A., et al.
(författare)
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Large Bergman spaces : invertibility, cyclicity, and subspaces of arbitrary index
- 2004
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 207:1, s. 111-160
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Tidskriftsartikel (refereegranskat)abstract
- In a wide class of weighted Bergman spaces, we construct invertible non-cyclic elements. These are then used to produce z-invariant subspaces of index higher than one. In addition, these elements generate non-trivial bilaterally invariant subspaces in anti-symmetrically weighted Hilbert spaces of sequences.
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| 3. |
- Chanillo, S., et al.
(författare)
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Nonlinear eigenvalues and analytic hypoellipticity
- 2004
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 209:2, s. 425-443
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by the problem of analytic hypoellipticity, we show that a special family of compact non-self-adjoint operators has a nonzero eigenvalue. We recover old results obtained by ordinary differential equations techniques and show how it can be applied to the higher dimensional case. This gives in particular a new class of hypoelliptic, but not analytic hypoelliptic operators.
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| 4. |
- Gustafsson, Björn, et al.
(författare)
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Restriction operators, balayage and doubly orthogonal systems of analytic functions
- 2003
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Ingår i: Journal of Functional Analysis. - 0022-1236 .- 1096-0783. ; 199:2, s. 332-378
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Tidskriftsartikel (refereegranskat)abstract
- Systems of analytic functions which are simultaneously orthogonal over each of two domains were apparently first studied in particular cases by Walsh and Szego, and in full generality by Bergman. In principle, these are very interesting objects, allowing application to analytic continuation that is not restricted (as Weierstrassian continuation via power series) either by circular geometry or considerations of locality. However, few explicit examples are known, and in general one does not know even gross qualitative features of such systems. The main contribution of the present paper is to prove qualitative results in a quite general situation. It is by now very well known that the phenomenon of double orthogonality is not restricted to Bergman spaces of analytic functions, nor even indeed has it any intrinsic relation to analyticity; its essence is an eigenvalue problem arising whenever one considers the operator of restriction on a Hilbert space of functions on some set, to a subset thereof, provided this restriction is injective and compact. However, in this paper only Hilbert spaces of analytic functions are considered, especially Bergman spaces. In the case of the Hardy spaces Fisher and Micchelli discovered remarkable qualitative features of doubly orthogonal systems, and we have shown how, based on the classical potential-theoretic notion of balayage, and its modern generalizations, one can deduce analogous results in the Bergman space set-up, but with restrictions imposed on the geometry of the considered domains and measures; these were not needed in the Fisher-Micchelli analysis, but are necessary here as shown by examples. From a more constructive point of view we study the Bergman restriction operator between the unit disk and a compactly contained quadrature domain and show that the representing kernel of this operator is rational and it is expressible (as an inversion followed by a logarithmic derivative) in terms of the polynomial equation of the boundary of the inner domain.
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| 5. |
- Maligranda, Lech, et al.
(författare)
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On interpolation between L[1]+L[]∞ and L[1]∩L[]∞
- 1992
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Ingår i: Journal of Functional Analysis. - 0022-1236 .- 1096-0783. ; 107:2, s. 342-351
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Tidskriftsartikel (refereegranskat)abstract
- The couple {L1 + L∞, L1 ∩ L∞} is not a Calderón couple and the K-orbit of any element is described as a sum of two Marcinkiewicz spaces but the interpolation orbit is a sum of a Marcinkiewicz space and an Orlicz space.
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| 6. |
- Agmon, Shmuel, et al.
(författare)
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Persistence of embedded eigenvalues
- 2011
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 261:2, s. 451-477
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Tidskriftsartikel (refereegranskat)abstract
- We consider conditions under. which an embedded eigenvalue of a self-adjoint operator remains embedded under small perturbations. In the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m < infinity we show that in favorable situations, the set of small perturbations of a suitable Banach space which do not remove the eigenvalue form a smooth submanifold of codimension in. We also have results regarding the cases when the eigenvalue is degenerate or when the multiplicity of the continuous spectrum is infinite.
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| 7. |
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| 8. |
- Aleksandrov, Alexei, et al.
(författare)
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Finite rank Toeplitz operators: some extensions of D. Luecking's theorem.
- 2009
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 256:7, s. 2291-2303
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Tidskriftsartikel (refereegranskat)abstract
- The recent theorem by D. Luecking about finite rank Bergman-Toeplitz operators is extended to weights being distributions with compact support and to the spaces of harmonic functions. © 2008 Elsevier Inc. All rights reserved.
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| 9. |
- Aleman, Alexandru, et al.
(författare)
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Hilbert spaces of analytic functions with a contractive backward shift
- 2019
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 277:1, s. 157-199
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Tidskriftsartikel (refereegranskat)abstract
- We consider Hilbert spaces of analytic functions in the disk with a normalized reproducing kernel and such that the backward shift is a contraction on the space. We present a model for this operator and use it to prove the surprising result that functions which extend continuously to the closure of the disk are dense in the space. This has several applications, for example we can answer a question regarding reverse Carleson embeddings for these spaces. We also identify a large class of spaces which are similar to the de Branges–Rovnyak spaces and prove some results which are new even in the classical case.
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| 10. |
- Allaire, G., et al.
(författare)
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Homogenization and concentration for a diffusion equation with large convection in a bounded domain
- 2012
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 262:1, s. 300-330
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Tidskriftsartikel (refereegranskat)abstract
- We consider the homogenization of a non-stationary convection–diffusion equation posed in a bounded domain with periodically oscillating coefficients and homogeneous Dirichlet boundary conditions. Assuming that the convection term is large, we give the asymptotic profile of the solution and determine its rate of decay. In particular, it allows us to characterize the “hot spot”, i.e., the precise asymptotic location of the solution maximum which lies close to the domain boundary and is also the point of concentration. Due to the competition between convection and diffusion, the position of the “hot spot” is not always intuitive as exemplified in some numerical tests.
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