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作者：van den Ban, E. P.; Schlichtkrull, H.
摘要：Let X = G/H be a reductive symmetric space and K a maximal compact subgroup of G. The image under the Fourier transform of the space of K-finite compactly supported smooth functions on X is characterized.
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作者：Moore, Justin Tatch
摘要：In this paper I will show that it is relatively consistent with the usual axioms of mathematics (ZFC) together with a strong form of the axiom of infinity (the existence of a supercompact cardinal) that the class of uncountable linear orders has a five element basis. In fact such a basis follows from the Proper Forcing Axiom, a strong form of the Baire Category Theorem. The elements are X, w(1), w(2), C, C* where X is any suborder of the reals of cardinality N-1 and C is any Countryman line. T...
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作者：Banagl, Markus
摘要：Characteristic classes for oriented pseudomanifolds can be defined using appropriate self-dual complexes of sheaves. On non-Witt spaces, self-dual complexes compatible to intersection homology are determined by choices of Lagrangian structures at the strata of odd codimension. We prove that the associated signature and L-classes are independent of the choice of Lagrangian structures, so that singular spaces with odd codimensional strata, such as e.g. certain compactifications of locally symmet...
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作者：Forstneric, Franc
摘要：We prove that the classical Oka property of a complex manifold Y, concerning the existence and homotopy classification of holomorphic mappings from Stein manifolds to Y, is equivalent to a Runge approximation property for holomorphic maps from compact convex sets in Euclidean spaces to Y.
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作者：Beresnevich, Victor; Velani, Sanju
摘要：A Hausdorff measure version of the Duffin-Schaeffer conjecture in metric number theory is introduced and discussed. The general conjecture is established modulo the original conjecture. The key result is a Mass Transference Principle which allows us to transfer Lebesgue measure theoretic statements for lim sup subsets of R-k to Hausdorff measure theoretic statements. In view of this, the Lebesgue theory of lim sup sets is shown to underpin the general Hausdorff theory. This is rather surprisin...
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作者：De Faria, Edson; De Melo, Welington; Pinto, Alberto
摘要：In this paper we extend M. Lyubich's recent results on the global hyperbolicity of renormalization of quadratic-like germs to the space of C-r unimodal maps with quadratic critical point. We show that in this space the bounded-type limit sets of the renormalization operator have an invariant hyperbolic structure provided r >= 2 + alpha with alpha close to one. As an intermediate step between Lyubich's results and ours, we prove that the renormalization operator is hyperbolic in a Banach space ...
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作者：Hughes, Dominic J. D.
摘要：a Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional calculus (propositional logic) in which proofs are combinatorial (graph-theoretic), rather than syntactic. It defines a combinatorial proof of a proposition phi as a graph homomorphism h: C -> G(phi), where G(phi) is a graph associated with phi and C is a coloured graph. The main theorem is soundness and completeness: phi is true if and only if there ex...
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作者：Fefferman, Charles
摘要：Let f be a real-valued function on a compact set in R-n, and let m be a positive integer. We show how to decide whether f extends to a C-m function on R-n.
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作者：Wilking, Burkhard
摘要：There are very few examples of Riemannian manifolds with positive sectional curvature known. In fact in dimensions above 24 all known examples are diffeomorphic to locally rank one symmetric spaces. We give a partial explanation of this phenomenon by showing that a positively curved, simply connected, compact manifold (M,g) is up to homotopy given by a rank one symmetric space, provided that its isometry group Iso(M,g) is large. More precisely we prove first that if dim(Iso(M,g)) >= 2 dim(M) -...
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作者：Bayer-Fluckiger, E.; Parimala, R.
