ODE to L^p norms

2014/02/03 by Jarno Talponen, Talponen, Jarno
Engineering · #31B10 #34A12 #46B10 #46E30 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1402.0528

openalex publication_date 2014/02/03 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this paper we relate the geometry of Banach spaces to the theory of differential equations, apparently in a new way. We will construct Banach function space norms arising as weak solutions to ordinary differential equations of first order. This provides as a special case a new way of defining varying exponent L^p spaces, different from the Orlicz type approach. We explain heuristically how the definition of the norm by means of the particular ODE is justified. The resulting class of spaces includes the classical L^p spaces as a special case. We present an ODE-free means of defining the norms investigated.

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