منابع مشابه
A note on spectral mapping theorem
This paper aims to present the well-known spectral mapping theorem for multi-variable functions.
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Let A,B be nonempty subsets of a an abelian group G. Let Ni(A,B) denote the set of elements of G having i distinct decompositions as a product of an element of A and an element of B. We prove that ∑ 1≤i≤t |Ni(A,B)| ≥ t(|A|+ |B| − t− α+ 1 + w) − w, where α is the largest size of a coset contained in AB and w = min(α − 1, 1), with a strict inequality if α ≥ 3 and t ≥ 2, or if α ≥ 2 and t = 2. Thi...
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“Weyl’s theorem holds” for an operator T on a Banach space X when the complement in the spectrum of the “Weyl spectrum” coincides with the isolated points of spectrum which are eigenvalues of finite multiplicity. This is close to, but not quite the same as, equality between the Weyl spectrum and the “Browder spectrum”, which in turn ought to, but does not, guarantee the spectral mapping theorem...
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Goodman's theorem states that intuitionistic arithmetic in all nite types plus full choice, HA ! + AC, is conservative over rst-order intuitionistic arithmetic HA. We show that this result does not extend to various subsystems of HA ! , HA with restricted induction.
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A classical result of Tchakaloff on the existence of exact quadrature formulae up to a given degree is extended to positive measures without compact support. A criterion for the existence of Gaussian quadratures for a class of such measures is also derived from the main proof.
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ژورنال
عنوان ژورنال: The Mathematical Gazette
سال: 1908
ISSN: 0025-5572
DOI: 10.2307/3603121