5 citations · 13 across the 14 of their papers we have counts for
14 papers
Orthogonal Polynomials, a Szegő--Verblunsky Theorem and Baxter's Theorem on the Quaternionic Sphere
Connor J. Gauntlett, David P. Kimsey
We introduce a theory of orthogonal polynomials on the unit sphere of the quaternions based on the notion of a -positive measure (which originated in a work of Alpay, Colombo, t…
Orthogonal Polynomials, Verblunsky Coefficients, and a Szegő-Verblunsky Theorem on the Unit Sphere in
Connor J. Gauntlett, David P. Kimsey
Given a measure on the unit sphere in with Lebesgue decomposition , with respect to the rotation-i…
A Noncommutative Szegő-Type Theorem on the Row-Ball
Connor J. Gauntlett, David P. Kimsey
In this paper we leverage the recently developed theory of noncommutative (nc) measures to prove a free noncommutative analogue of many known equalities extending the weak Szegő li…
Moment indeterminateness: the Marcel Riesz variational principle
David P. Kimsey, Mihai Putinar
The discrete data encoded in the power moments of a positive measure, fast decaying at infinity on euclidean space, is incomplete for recovery, leading to the concept of moment ind…
The spectral theorem for normal operators on a Clifford module
Fabrizio Colombo, David P. Kimsey
In this paper, using the recently discovered notion of the -spectrum, we prove the spectral theorem for a bounded or unbounded normal operator on a Clifford module (i.e., a two-…
Universality property of the -functional calculus, noncommuting matrix variables and Clifford operators
Fabrizio Colombo, Jonathan Gantner, David P. Kimsey +1
The spectral theory on the -spectrum was born out of the need to give quaternionic quantum mechanics (formulated by Birkhoff and von Neumann) a precise mathematical foundation.…
On a minimal solution for the indefinite truncated multidimensional moment problem
David P. Kimsey
We will consider the indefinite truncated multidimensional moment problem. Necessary and sufficient conditions for a given truncated multisequence to have a signed representing mea…
The moment problem on curves with bumps
David Kimsey, Mihai Putinar
The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the…
Functions of the infinitesimal generator of a strongly continuous quaternionic group
Daniel Alpay, Fabrizio Colombo, Jonathan Gantner +1
The analogue of the Riesz-Dunford functional calculus has been introduced and studied recently as well as the theory of semigroups and groups of linear quaternionic operators. In t…
Wiener algebra for the quaternions
Daniel Alpay, Fabrizio Colombo, David P. Kimsey +1
We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-Lévy type theorem and a factoriz…
The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum
Daniel Alpay, Fabrizio Colombo, David P. Kimsey
In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of -spectrum. The proof technique consists of first establishing a spect…
Boundary interpolation for slice hyperholomorphic Schur functions
K. Abu-Ghanem, D. Alpay, F. Colombo +2
A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers , quaternions …
The spectral theorem for unitary operators based on the -spectrum
D. Alpay, F. Colombo, D. P. Kimsey +1
The quaternionic spectral theorem has already been considered in the literature, see e.g. [22], [31], [32], however, except for the finite dimensional case in which the notion of s…
An extension of Herglotz's theorem to the quaternions
D. Alpay, F. Colombo, D. P. Kimsey +1
A classical theorem of Herglotz states that a function from into is positive definite if and only there exists a $\mathbb C^{s\t…