Prolate spheroidal wave functions, Sonine spaces, and the Riemann zeta function

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:389

Article

Li, Xian-Jin

关键词: Explicit formula;    Orthogonal projections;    Special functions;   

DOI  :  10.1016/j.jmaa.2011.11.068

来源: Elsevier

【 摘 要 】

In this paper we study underlying spaces associated with A. Connes' trace formula (see Connes (1999) [3], Li (2010) [14]). In particular the explicit formula in the theory of prime numbers is expressed as the trace of an operator acting on a Hilbert space, which is a direct sum of a Sonine space, the space of prolate spheroidal wave functions, and a variant of the space of prolate spheroidal wave functions. A formula is obtained for the orthogonal projection of the Hilbert space onto the Sonine space. A base is given for the variant space of the space of prolate spheroidal wave functions. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free