Paper's Title:

Pointwise Convergence of Fourier-type Series with Exponential Weights

Author(s):

Hee Sun Jung and Ryozi Sakai

Department of Mathematics Education, Sungkyunkwan University,
Seoul 110-745,
Republic of Korea.
E-mail: hsun90@skku.edu

Department of Mathematics,
Meijo University, Nagoya 468-8502,
Japan.
E-mail: ryozi@hm.aitai.ne.jp

Abstract:

Let R = ( - ∞,∞), and let Q∈C¹(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 Fourier-type series with respect to the orthonormal polynomials {p_n(w²;x)}.

Paper's Title:

Applications of Von Neumann Algebras to Rigidity Problems of (2-Step) Riemannian (Nil-)Manifolds

Author(s):

Atefeh Hasan-Zadeh and Hamid-Reza Fanai

DFouman Faculty of Engineering,
College of Engineering, University of Tehran,
Iran.
E-mail: hasanzadeh.a@ut.ac.ir

Department of Mathematical Sciences,
Sharif University of Technology,
Iran
E-mail: 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 2-step nilmanifolds.

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