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Eigenvalues of Weakly Singular Integral Operators
Author(s) -
Cobos Fernando,
Kühn Thomas
Publication year - 1990
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-41.2.323
Subject(s) - mathematics , logarithm , gravitational singularity , singularity , eigenvalues and eigenvectors , conjecture , dimension (graph theory) , order (exchange) , pure mathematics , domain (mathematical analysis) , mathematical analysis , physics , finance , quantum mechanics , economics
We determine the asymptotic order of decay of eigenvalues of weakly singular integral operators. The singularities are of quite general form, containing power and logarithmic terms. We give a unified elementary proof of all known results in this area. Our approach applies also in the case where the power order of the singularity is equal to the dimension of the domain and the logarithmic order is less than −1. This case has not been considered previously. Furthermore, we show the optimality of the upper estimates in a rather strong sense. In particular, we give a partial positive answer to the conjecture of [ 3 ].