Holomorphic Hermite functions and ellipses

Schwartz functions, Hermite functions, and the Hermite operator

Monotonicity and holomorphic functions

This is a survey on some recent works, mainly by the author on the relation between holomorphic functions on Kähler manifolds, monotonicity and the geometry of complex manifolds. We also use this opportunity to give details of a sketched step in the proof of a previously established result. Math Subject Classifications. Primary: 58G11, 53C44.

Hermite functions

We define S to be the set of those φ ∈ C∞(R,C) such that pn(φ) < ∞ for all n ≥ 0. S is a complex vector space and each pn is a norm, and because each pn is a norm, a fortiori {pn : n ≥ 0} is a separating family of seminorms. With the topology induced by this family of seminorms, S is a Fréchet space. As well, D : S → S defined by (Dφ)(x) = φ′(x), x ∈ R 1http://individual.utoronto.ca/jordanbell/...

From Holomorphic Functions to Holomorphic Sections

It is a pleasure to have the opportunity in the graduate colloquium to introduce my research field. I am a differential geometer. To be more precise, I am a complex differential geometer, although I am equally interested in real differential geometry. To many people, geometry is a kind of mathematics that is related to length, area, volume, etc. For the Euclidean geometry, this is indeed the ca...

Hermite Orthogonal Rational Functions

We recount previous development of d-fold doubling of orthogonal polynomial sequences and give new results on rational function coefficients, recurrence formulas, continued fractions, Rodrigues’ type formulas, and differential equations, for the general case and, in particular, for the d-fold Hermite orthogonal rational functions.