31 citations · 108 across the 23 of their papers we have counts for
10 papers · 1 filter
Foundations for proper-time relativistic quantum theory
Tepper L. Gill, Trey Morris, Stewart K. Kurtz
This paper is a progress report on the foundations for the canonical proper-time approach to relativistic quantum theory. We first review the the standard square-root equation of r…
Global solutions to the homogeneous and inhomogeneous Navier-Stokes equations
Tepper L. Gill, Daniel Williams, Woodford W. Zachary
In this paper we take a new approach to a proof of existence and uniqueness of solutions for the 3D-Navier-Stokes equations, which leads to essentially the same proof for both boun…
Note on the Spectral Theorem
Tepper L Gill, Daniel Williams
In this note, we show that the spectral theorem, has two representations; the Stone-von Neumann representation and one based on the polar decomposition of linear operators, which w…
Adjoint Operators on Banach Spaces
Tepper L Gill, Francis Mensah, Woodford W. Zachary
In this paper, we report on new results related to the existence of an adjoint for operators on separable Banach spaces and discuss a few interesting applications. (Some results ar…
Two Mathematically Equivalent Versions of Maxwell's Equations
Tepper L. Gill, Woodford W. Zachary
This paper is a review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics. The purpose is to provide a physically complete classical back…
Global (in Time) Solutions to the 3D-Navier-Stokes Equations on R^3
Tepper L Gill, Woodford W. Zachary
A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possib…
Constructive Representation Theory for the Feynman Operator Calculus
Tepper L Gill, Woodford W Zachary
In this paper, we survey recent progress on the constructive theory of the Feynman operator calculus. (The theory is constructive in that, operators acting at different times, actu…
Sufficiency Class for Global (in Time) Solutions to the 3D-Navier-Stokes Equations
Tepper L Gill, Woodford W. Zachary
A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possib…
Adjoint for Operators in Banach Spaces
T. L. Gill, S. Basu, W. W. Zachary +1
In this paper we show that a result of Gross and Kuelbs, used to study Gaussian measures on Banach spaces, makes it possible to construct an adjoint for operators on separable Bana…
Foundations for Relativistic Quantum Theory I: Feynman's Operator Calculus and the Dyson Conjectures
T. L. Gill, W. W Zachary
In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We sh…