Functions and Analysis

2502 Submissions

[4] viXra:2502.0090 [pdf] replaced on 2025-12-12 11:44:02

A Story of a Function

Authors: Andrej Liptaj
Comments: 24 Pages.

We dedicate this text to a study of a function with interesting properties: besides being, by construction, well suited for a certain type of approximations, the function happens to be lacunary, i.e. without analytic continuation outside the complex unit disk. It however satisfies a functional equation which can be (with some restriction) solved everywhere except the origin. Unfortunately, this solution cannot be understood as its natural continuation beyond the disk.
Category: Functions and Analysis

[3] viXra:2502.0078 [pdf] submitted on 2025-02-12 20:49:58

Find[ing] the Functional Dependency Relationship Between Functions

Authors: José Manuel Gómez Vega
Comments: 19 Pages. Licence CC BY-NC

An algorithmic method is proposed to solve functional dependency relationships between functions. To do so, a simple theorem is stated and three examples are provided, including the solutionto demonstrate the effectiveness of the method.
Category: Functions and Analysis

[2] viXra:2502.0075 [pdf] submitted on 2025-02-11 10:03:23

A Study of Continuous Frames and Operators in Quaternionic Hilbert Spaces

Authors: Najib Khachiaa
Comments: 20 Pages.

The aim of this work is to study continuous frame theory in quaternionic Hilbert spaces. We provide a characterization of continuous frames in these spaces through the associated operators. Additionally, we examine continuous frames of the form $LF:Omegaightarrow mathcal{H}$, where $(Omega,mu)$ is a measure space, $L:mathcal{H}ightarrow mathcal{H}$ is a right $mathbb{H}$-linear bounded operator and $F:Omegaightarrow mathcal{H}$ is a continuous frame for $mathcal{H}$.
Category: Functions and Analysis

[1] viXra:2502.0045 [pdf] replaced on 2025-03-17 02:18:09

Solution to the Problem on the Existence and Smoothness of the Navier-Stokes Equations

Authors: Daniel Thomas Hayes
Comments: 6 Pages. (Note by viXra Admin: Frequent replacement may not be accepted)

The Navier--Stokes equations are used to describe viscous incompressible fluid flow. It has been on the list of the Clay Mathematics Institute’s millennium prize problems to decide whether or not physically reasonable solutions to the Navier--Stokes equations do in general exist. In this paper, the problem on the existence and smoothness of the Navier--Stokes equations is solved. It is proven that the Navier--Stokes equations are globally regular.
Category: Functions and Analysis