Functions Defined at Infinity and Normal Behavior

Paper Title:

Functions Analytic at Infinity and Normality

Published on:

14 March 2024

Primary Category:

Mathematical Physics

Paper Authors:

Tristram de Piro

Bullets

Key Details

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Defines functions analytic at infinity via convergent power series for large inputs

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Considers functions with very moderate and moderate decrease rates

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Defines quasi normal and quasi split normal classes of well-behaved functions

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Gives examples like the Newtonian potential and proves they are normal

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Shows Fourier transforms can be defined for these function classes

Explore the topics in this paper

analytic functions

fourier transforms

function classes

large inputs

power series

AI generated summary

Functions Defined at Infinity and Normal Behavior

This paper explores the notion of functions that are analytic at infinity, meaning they have convergent power series representations for large inputs. Several classes of well-behaved functions are defined, including those with very moderate decrease, moderate decrease, quasi normal, and quasi split normal. Examples are given, and key properties like the existence of Fourier transforms are established.