Bounded $J$-fractions and univalence.

Structuralism, Invariance, and Univalence

The recent discovery of an interpretation of constructive type theory into abstract homotopy theory suggests a new approach to the foundations of mathematics with intrinsic geometric content and a computational implementation. Voevodsky has proposed such a program, including a new axiom with both geometric and logical significance: the Univalence Axiom. It captures the familiar aspect of inform...

Decomposing the Univalence Axiom

This paper investigates the univalence axiom in intensional Martin-Löf type theory. In particular, it looks at how univalence can be derived from simpler axioms. We first present some existing work, collected together from various published and unpublished sources; we then we present a new decomposition of the univalence axiom into simpler axioms. We argue that these axioms are easier to verify...

On the Convergence of Bounded J{fractions on the Resolvent Set of the Corresponding Second Order Diierence Operator

We study connections between continued fractions of type J and spectral properties of second order diierence operators with complex coeecients. It is known that the convergents of a bounded J{fraction are diagonal Pad e approximants of the Weyl function of the corresponding diierence operator, and that a bounded J{fraction converges uniformly to the Weyl function in some neighborhood of innnity...

Univalence of Certain Integral Operators

We study some integral operators and determine conditions for the univalence of these integral operators.

Univalence conditions and Sturm-Liouville eigenvalues