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1999•Proceedings of the Royal Society A Mathematical Physical and Engineering SciencesRequires access

On the existence of an eigenvalue below the essential spectrum

B. Malcolm Brown, Daniel K. R. McCormack, Anton Zettl

Open publisher page 7 citations

Abstract

This paper is concerned with a computer–assisted proof of eigenvalues below the essential spectrum of the Sturm–Liouville problem on the half–line. It uses methods of functional analysis and interval analysis to derive algorithms that may be used to prove the existence of such eigenvalues.

About this research paper

What this paper is about

This paper is concerned with a computer–assisted proof of eigenvalues below the essential spectrum of the Sturm–Liouville problem on the half–line. It uses methods of functional analysis and interval analysis to derive algorithms that may be used to prove the existence of such eigenvalues.

Why it matters

OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper is concerned with a computer–assisted proof of eigenvalues below the essential spectrum of the Sturm–Liouville problem on the half–line. It uses methods of functional analysis and interval analysis to derive algorithms that may be used to prove the existence of such eigenvalues.

Key concepts: Eigenvalues and eigenvectors, Spectrum (functional analysis), Mathematics, Interval (graph theory), Line (geometry), Spectrum of a matrix, Essential spectrum, Real line

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