Ramifications, old and new, of the eigenvalue problem

1950/01/01 by Hermann Weyl · 6 citations
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Matrix Theory and Algorithms #Advanced Mathematical Modeling in Engineering #Eigenvalues and eigenvectors #Mathematics #Applied mathematics #Physics #Quantum mechanics

paper · pdf · doi:10.1090/s0002-9904-1950-09369-0

openalex publication_date 1950/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07

Abstract

Since this is a lecture dedicated to the memory of Josiah Willard Gibbs let me start with that purely mathematical discovery which Gibbs contributed to the theory of Fourier series. Fourier series have to do with the eigenvalues and eigenfunctions of the oldest, simplest, and most important of all spectrum problems, that of the vibrating string. In preparing this lecture, the speaker has assumed that he is expected to talk on a subject in which he had some first-hand experience through his own work. And glancing back over the years he found that the one topic to which he has returned again and again is the problem of eigenvalues and eigenfunctions in its various ramifications. It so happens that right at the beginning of my mathematical career I wrote two papers on what we now call the Gibbs phenomenon.

Citations

• �ber gew�hnliche Differentialgleichungen mit Singularit�ten und die zugeh�rigen Entwicklungen willk�rlicher Funktionen

Cited by

• The Asymptotic Distribution of Eigenvalues and Eigenfunctions for Elliptic Boundary Value Problems
• The uncertainty principle
• Decoherence and Wave Function Collapse
• Effective Lagrangian and energy-momentum tensor in de Sitter space
• Spectral theory for perturbed Krein Laplacians in nonsmooth domains
• Hermann Weyl [wikipedia]