Szegö theorems for Zoll operators

Szegö limit theorems for operators with almost periodic diagonals Steffen

The classical Szegö theorems study the asymptotic behaviour of the determinants of the finite sections PnT (a)Pn of Toeplitz operators, i.e., of operators which have constant entries along each diagonal. We generalize these results to operators which have almost periodic functions on their diagonals.

Lower Order Terms in Szegö Theorems on Zoll Manifolds

We give an outline of the computation of the third order term in a generalization of the Strong Szegö Limit Theorem for a zeroth order pseudodifferential operator (PsDO) on a Zoll manifold of an arbitrary dimension, see [Gi2] for the detailed proof. This is a refinement of a result by V. Guillemin and K. Okikiolu who have computed the second order term in [GO2]. An important role in our proof i...

Szegö Kernels, Toeplitz Operators, and Equivariant Fixed Point Formulae

The aim of this paper is to apply algebro-geometric Szegö kernels to the asymptotic study of a class of trace formulae in equivariant geometric quantization and algebraic geometry. Let (M,J) be a connected complex projective manifold, of complex dimension d, and let A be an ample line bundle on it. Let, in addition, G be a compact and connected g-dimensional Lie group acting holomorphically on ...

Saturation theorems for diseretized linear operators

There is a well developed theory of saturation for positive convolution operators on C*, the space of 2n-periodic and continuous functions. Up until recently, this was suitable to handle almost all the important approximation processes on C*. Now, however, some new and interesting sequences of operators have been obtained for C* by discretizing convolution operators [1], [5]. Such a discretized...

Fixed point theorems for sums of operators