8 papers
A Monte Carlo Estimator for an Isolated Polynomial Zero via Contour Integral Representations
Athanasios Christou Micheas
We introduce a Monte Carlo approach for estimating isolated polynomial zeros through their contour integral representations. For a simple zero enclosed by an isolating contour, we…
A proof of Riemann's hypothesis via Hadamard-Weierstrass factorization
Athanasios Christou Micheas
Using the Hadamard-Weierstrass factorization theorem for Riemann's ξ function, we discuss and prove Riemann's hypothesis.
The Taylor Integral and a Generalization of the Discrete Fourier Transform
Athanasios Christou Micheas
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particu…
Zeroes and Extrema of Functions via Random Measures
Athanasios Christou Micheas
We present methods that provide all zeroes and extrema of a function that do not require differentiation. Using point process theory, we are able to describe the locations of zeroe…
The Taylor Measure and its Applications
Athanasios Christou Micheas
We propose and study a novel collection of signed measures, which will be apply called Taylor measures. Stochastic versions of the new measures are also defined and studied. We ill…
Stochastic Taylor expansion via Poisson point processes
Weichao Wu, Athanasios C. Micheas
We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear re…
The Multivariate Taylor Measure Function Space and a Generalization of Taylor's Theorem
Athanasios Christou Micheas
Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. W…
The Wronski orthogonalization process in Hilbert function spaces
Athanasios Christou Micheas
Based on the Wronski determinant, we propose the construction of linearly independent and orthogonal functions in any Hilbert function space. We call the new method the Wronski ort…