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D. E. Edmunds

Publications and source records attributed to D. E. Edmunds.

4 recordsLinked to original sources
arXiv2025

The EPR Paradox of Quantum Mechanics in the Light of Four Unpublished Letters between A. Einstein and the Mathematician J. L. B. Cooper

This paper presents correspondence between Albert Einstein and the mathematical analyst J. L. B. Cooper on the Einstein-Podolsky-Rosen (EPR) paradox of quantum theory published in 1935. Two letters written by Cooper, and the replies from Einstein, all written between October and December 1949, are retyped from the original ones. Furthermore, Einstein's second letter, which he wrote in German, is translated into English. The lack of agreement, arising from very different points of view, is analysed, taking into account the complex underlying mathematical and physical factors that arise naturally in connection with the EPR paradox.

physics.hist-ph↗
arXiv2022

Almost-compact and compact embeddings of variable exponent spaces

Let $Ω$ be an open subset of $\mathbb{R}^{N}$, and let $p,\, q:Ω\rightarrow \left[ 1,\infty \right] $ be measurable functions. We give a necessary and sufficient condition for the embedding of the variable exponent space $L^{p(\cdot )}\left( Ω\right) $ in $L^{q(\cdot )}\left( Ω\right) $ to be almost compact. This leads to a condition on $Ω, \, p$ and $q$ sufficient to ensure that the Sobolev space $W^{1,p(\cdot )}\left( Ω\right) $ based on $L^{p(\cdot )}\left( Ω\right) $ is compactly embedded in $L^{q(\cdot )}\left( Ω\right) ;$ compact embedding results of this type already in the literature are included as special cases.

math.FA↗
arXiv2021

Remarks on j-eigenfunctions of operators

The paper is largely concerned with the possibility of obtaining a series representation for a compact linear map $T$ acting between Banach spaces. It is known that, using the notions of $j-$eigenfunctions and $j-$% eigenvalues, such a representation is possible under certain conditions on $T$. Particular cases discussed include those in which $T$ can be factorised through a Hilbert space, or has certain $s$-numbers that are fast-decaying. The notion of $p-$compactness proves to be useful in this context; we give examples of maps that possess this property.

math.FA↗