Prof. F. Riesz

The theorem of F. and M. Riesz

Suppose that G is a locally compact abelian group and that P ⊂ G is a semigroup (satisfies P + P ⊂ P ) that is closed and satisfies P ∩ (−P ) = {0} and P ∪ (−P ) = G. We define a total order on G by x ≤ y when y − x ∈ P . We verify that this is indeed a total order. (We remark that nowhere in this do we show the significance of P being closed; but in this note we shall be speaking about discret...

Prof. Dr. Prof. Prof.

Riesz Logic

We introduce Riesz Logic, whose models are abelian lattice ordered groups, which generalise Riesz spaces (vector lattices), and show soundness and completeness. Our motivation is to provide a logic for distributional semantics of natural language, where words are typically represented as elements of a vector space whose dimensions correspond to contexts in which words may occur. This basis prov...

Riesz Composition

We give a suucient condition for a univalently induced composition operator on the Hardy space H 2 to be a Riesz operator. We then establish that every Riesz composition operator has a Koenigs model and explore connections our work has with the model theory and spectral theory of composition operators.

A Kotz-Riesz-Type Distribution

This article derives the distribution of random matrix X associated with the transformation Y = X*X, such that Y has a Riesz distribution for real normed division algebras. Two versions of this distributions are proposed and some of their properties are studied.