منابع مشابه
Carleman Estimates and Absence of Embedded Eigenvalues
Let L = −∆− W be a Schrödinger operator with a potential W ∈ L n+1 2 (R), n ≥ 2. We prove that there is no positive eigenvalue. The main tool is an L − Lp′ Carleman type estimate, which implies that eigenfunctions to positive eigenvalues must be compactly supported. The Carleman estimate builds on delicate dispersive estimates established in [7]. We also consider extensions of the result to var...
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A sharpened version of Carleman’s inequality is proved. This result unifies and generalizes some recent results of this type. Also the “ordinary” sum that serves as the upper bound is replaced by the corresponding Cesaro sum. Moreover, a Carleman type inequality with a more general measure is proved and this result may also be seen as a generalization of a continuous variant of Carleman’s inequ...
متن کاملGlobal Carleman estimates for waves and applications
Abstract In this article, we extensively develop Carleman estimates for the wave equation and give some applications. We focus on the case of an observation of the flux on a part of the boundary satisfying the Gamma conditions of Lions. We will then consider two applications. The first one deals with the exact controllability problem for the wave equation with potential. Following the duality m...
متن کاملQuasianalytic Denjoy-carleman Classes and O-minimality
The work in this paper has been motivated by two questions from the theory of o-minimality (see for instance [6]): (1) Does every o-minimal expansion of the real field admit analytic cell decomposition? (2) Does there exist a “largest” o-minimal expansion M of the real field, in the sense that any other o-minimal expansion of the real field is a reduct of M? We describe here a new method of con...
متن کاملInvariant Functions in Denjoy–carleman Classes
Let V be a real finite dimensional representation of a compact Lie group G. It is well-known that the algebra R[V ] of G-invariant polynomials on V is finitely generated, say by σ1, . . . , σp. Schwarz [38] proved that each G-invariant C-function f on V has the form f = F (σ1, . . . , σp) for a Cfunction F on R. We investigate this representation within the framework of Denjoy–Carleman classes....
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ژورنال
عنوان ژورنال: Historia Mathematica
سال: 1987
ISSN: 0315-0860
DOI: 10.1016/0315-0860(87)90048-6