


Paper's Title:
Pointwise Convergence of Fouriertype Series with Exponential Weights
Author(s):
Hee Sun Jung and Ryozi Sakai
Department of Mathematics Education,
Sungkyunkwan University,
Seoul 110745,
Republic of Korea.
Email: hsun90@skku.edu
Department of Mathematics,
Meijo University, Nagoya 4688502,
Japan.
Email: ryozi@hm.aitai.ne.jp
Abstract:
Let R = (  ∞,∞), and let Q∈C^{1}(R):R→[0,∞) be an even function. We consider the exponential weights w(x)=e^{Q(x)}, x∈R. In this paper we obtain a pointwise convergence theorem for the Fouriertype series with respect to the orthonormal polynomials {p_{n}(w^{2};x)}.
Paper's Title:
Applications of Von Neumann Algebras to Rigidity Problems of (2Step) Riemannian (Nil)Manifolds
Author(s):
Atefeh HasanZadeh and HamidReza Fanai
DFouman Faculty of Engineering,
College of Engineering, University of Tehran,
Iran.
Email: hasanzadeh.a@ut.ac.ir
Department of Mathematical Sciences,
Sharif University of Technology,
Iran
Email: fanai@sharif.edu
Abstract:
In this paper, basic notions of von Neumann algebra and its direct analogues in the realm of groupoids and measure spaces have been considered. By recovering the action of a locally compact Lie group from a crossed product of a von Neumann algebra, other proof of one of a geometric propositions of O'Neil and an extension of it has been proposed. Also, using the advanced exploration of nilmanifolds in measure spaces and their corresponding automorphisms (Lie algebraic derivations) a different proof of an analytic theorem of Gordon and Mao has been attained. These two propositions are of the most important ones for rigidity problems of Riemannian manifolds especially 2step nilmanifolds.
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