arXiv subjects

Edoardo Niccolai

Publications and source records attributed to Edoardo Niccolai.

3 recordsLinked to original sources

arXiv2023

Stochastic Covariant Derivatives in a (Curved) Space-Time: a Glimpse into the Fractoid Spaces

A study on the notion of covariant derivatives in flat and curved space-time via Itô-Wiener processes, when subjected to stochastic processes, is presented. Going into details, there is an analysis of the following topics: (i) Besov space, (ii) Schrödinger operators, (iii) Klein-Gordon and Dirac equations, (iv) Dirac operator via Clifford connection, (v) semi-martingale and Stratonovich integral, (vi) stochastic geodesics, (vii) white noise on a (4+)D space-time $\mathfrak{H}$-geometry (with the Paley-Wiener integral), and (viii) torsion of the covariant derivative. In the background stands the scale relativity theory, together with a sketch of the concept of fractoid spaces.

math.PR↗

arXiv2023

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.

math-ph↗

arXiv2023

Bounded Mean Oscillation: an $\mathbb{R}$-Function with Multi-$\mathbb{K}_6$ Cubes. Dual of the Hardy Space $H^1$ and Banach Extent

This paper investigates the concept of harmonic functions of bounded mean oscillation, starting from John-Nirenberg's pioneering studies, under a renewed formalism, suitable for bringing out some fundamental properties inherent in it. In more detail: after a quick introduction, the second Section presents the main theorem, plus complete proof, relating to this function; in the third Section there is a suggestion on the exponential integrability (theorem and sketch of proof), while the fourth Section deals with the duality of Hardy Space $H^1$ and bounded mean oscillation, with some ideas for a demonstration. The writing closes with a graphic appendix.

math.FA↗