Mathematics – Functional Analysis
Scientific paper
2002-12-19
Comm. Partial Differential Equations 28 (2003), no. 9-10, 1739--1785.
Mathematics
Functional Analysis
39 pages, full version, submitted
Scientific paper
10.1081/PDE-120024531
This is a detailed version of the paper math.FA/0212273. The main motivation for this work was to find an explicit formula for a "Szego-regularized" determinant of a zeroth order pseudodifferential operator (PsDO) on a Zoll manifold. The idea of the Szego-regularization was suggested by V. Guillemin and K. Okikiolu. They have computed the second term in a Szego type expansion on a Zoll manifold of an arbitrary dimension. In the present work we compute the third asymptotic term in any dimension. In the case of dimension 2, our formula gives the above mentioned expression for the Szego-redularized determinant of a zeroth order PsDO. The proof uses a new combinatorial identity, which generalizes a formula due to G.A.Hunt and F.J.Dyson. This identity is related to the distribution of the maximum of a random walk with i.i.d. steps on the real line. The proof of this combinatorial identity together with historical remarks and a discussion of probabilistic and algebraic connections has been published separately.
No associations
LandOfFree
Lower order terms in Szego type limit theorems on Zoll manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Lower order terms in Szego type limit theorems on Zoll manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lower order terms in Szego type limit theorems on Zoll manifolds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-330521