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Trace Formulas for Some Singular Differential Operators and Applications
Author(s) -
Metafune Giorgio,
Pallara Diego
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/(sici)1522-2616(200003)211:1<127::aid-mana127>3.0.co;2-a
Subject(s) - mathematics , eigenfunction , trace (psycholinguistics) , eigenvalues and eigenvectors , differential operator , zero (linguistics) , mathematical analysis , hilbert space , constant coefficients , pure mathematics , degenerate energy levels , boundary value problem , order (exchange) , operator theory , philosophy , linguistics , physics , finance , quantum mechanics , economics
We characterize the convergence of the series ∑ λ –1 n , where λ n are the non‐zero eigenvalues of some boundary value problems for degenerate second order ordinary differential operators and we prove a formula for the above sum when the coefficient of the zero‐order term vanishes. We study these operators both in weighted Hilbert spaces and in spaces of continuous functions. After investigating the boundary behaviour of the eigenfunctions, we give applications to the regularity of the generated semigroups.