Compactness of isospectral sets
نویسندگان
چکیده
منابع مشابه
Compactness of isospectral sets
© Séminaire de Théorie spectrale et géométrie (Grenoble), 1991, tous droits réservés. L’accès aux archives de la revue « Séminaire de Théorie spectrale et géométrie » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fi...
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The Schrödinger operator −∆+V , of a compact Riemannian manifold M , has pure point spectrum. Suppose that V0 is a smooth reference potential. Various criteria are given which guarantee the compactness of all V satisfying spec(−∆+V ) = spec(−∆+V0). In particular, compactness is proved assuming an a priori bound on the Ws,2(M) norm of V , where s > n/2 − 2 and n = dimM . This improves earlier wo...
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We show that a number of contenders for an abstract and general notion of compactness, applicable in particular to computability theory and constructive mathematics, coincide in some well known frameworks. We consider compactness of sets rather than of spaces, where we replace topologies by the restriction to constructive reasoning, as in the work by a number of authors, including Penon, Dubuc,...
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0 κ0κ1 1 · · ·κ αk−1 k−1 ds , k ≥ 3 . Here ck 6= 0 and the sum, which is finite, consists of lower order terms in the sense that αk−1 ≤ 2. The bk+1 therefore bound the corresponding Sobolev norms on κ and the compactness, in the C∞ topology on κ, of the set of domains with a fixed spectrum follows. The coefficients a0, a1, a2, a3, b0, b1, b2 have already been computed, see L. Smith [5] and the ...
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ژورنال
عنوان ژورنال: Séminaire de théorie spectrale et géométrie
سال: 1991
ISSN: 2118-9242
DOI: 10.5802/tsg.111