Applied Mathematics by J. David Logan

Author:J. David Logan [Logan, J. David]
Language: eng
Format: epub, pdf
ISBN: 9781118501733
Publisher: Wiley
Published: 2013-06-18T04:00:00+00:00

Corollary 5.43

The Volterra operator (4.12) has no eigenvalues.

This result is consistent with our comment that Volterra equations come from initial value problems, and linear initial value problems for differential equations have no eigenvalues. The conclusion is in sharp contrast to Fredholm equations, which arise from boundary value problems. We already know that boundary value problems (e.g., Sturm–Liouville problems) have a rich spectral structure, and we expect the same from Fredholm operators.

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