In this paper we prove a $K$-homology index theorem for the Toeplitz operators obtained from multishifts of Bergman space on several classes egg-like domains. This generalizes our with Douglas and Yu unit ball.

0. Introduction. This paper extends some results from [1] and applies them to certain transformations of the unit interval. §§2-4 are concerned with symbolic dynamics and §§5-6 are concerned with their application to the proof of our main theorem which states sufficient conditions for a piecewise continuous transformation of the unit interval to be conjugate to a (uniformly) piecewise linear tr...

The notion of proof-net category defined in this paper is closely related to graphs implicit in proof nets for the multiplicative fragment without constant propositions of linear logic. Analogous graphs occur in Kelly’s and Mac Lane’s coherence theorem for symmetric monoidal closed categories. A coherence theorem with respect to these graphs is proved for proof-net categories. Such a coherence ...

Here we will present some deeper results in renewal theory such as a central limit theorem for counting processes, stationary versions of renewal processes, renewal equations, the key renewal theorem, weak convergence. 1 Central limit theorem for counting processes Consider a renewal process {t n : n ≥ 1} with iid interarrival times X n = t n − t n−1 , n ≥ 0, such that 0 < E(X) = 1/λ < ∞ and 0 ...

The notion of proof-net category defined in this paper is closely related to graphs implicit in proof nets for the multiplicative fragment without constant propositions of linear logic. Analogous graphs occur in Kelly’s and Mac Lane’s coherence theorem for symmetric monoidal closed categories. A coherence theorem with respect to these graphs is proved for proof-net categories. Such a coherence ...

As a follow-up of Haberl-Schuster’s “Asymmetric affine Lp Sobolev inequalities” and Cianchi-Lutwak-Yang-Zhang’s “Affine Moser-Trudinger and Morrey-Sobolev inequalities”, we establish sharp Moser-Trudinger and MorrySobolev inequalities induced by the positive part of a directional derivative on the unit Euclidean sphere. 1. Theorem In their 2009 JFA paper [1], Haberl-Schuster prove the following...