Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the optimal asymptotic eigenvalue behaviour of weakly singular integral operators


Authors: Fernando Cobos, Svante Janson and Thomas Kühn
Journal: Proc. Amer. Math. Soc. 113 (1991), 1017-1022
MSC: Primary 45C05; Secondary 47B10, 47G10
DOI: https://doi.org/10.1090/S0002-9939-1991-1060720-X
MathSciNet review: 1060720
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We improve the known results on eigenvalue distributions of weakly singular integral operators having (power) order of the singularity equal to half of the dimension of the underlying domain. Moreover we show that our results are the best possible.


References [Enhancements On Off] (What's this?)

  • [1] B. Carl and T. Kühn, Entropy and eigenvalues of certain integral operators, Math. Ann. 268 (1984), 127-136. MR 744332 (85e:47041)
  • [2] F. Cobos and T. Kühn, Entropy and eigenvalues of weakly singular integral operators, Integral Equations and Operator Theory 11 (1988), 64-86. MR 920735 (89a:47073)
  • [3] -, Eigenvalues of weakly singular integral operators, J. London Math. Soc. (2) 41 (1990), 323-335. MR 1067272 (91h:47053)
  • [4] I. C. Gohberg and M. G. Krein, Introduction to the theory of linear non-selfadjoint operators, Amer. Math. Soc., Providence, RI, 1969. MR 0246142 (39:7447)
  • [5] H. König, Some remarks on weakly singular integral operators, Integral Equations and Operator Theory 3 (1980), 397-407. MR 580715 (82b:47063)
  • [6] -, Eigenvalue distribution of compact operators, Birkhäuser, Basel, Boston, MA, and Stuttgart, 1986.
  • [7] H. König, J. R. Retherford, and N. Tomczak-Jaegermann, On the eigenvalues of $ (p,2)$-summing operators and constants associated to normed spaces, J. Funct. Anal. 37 (1980), 88-126. MR 576647 (81m:47033)
  • [8] G. P. Kostometov, Asymptotic behaviour of the spectrum of integral operators with a singularity on the diagonal, Math. USSR-Sb. 23 (1974), 417-424. MR 0361935 (50:14377)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 45C05, 47B10, 47G10

Retrieve articles in all journals with MSC: 45C05, 47B10, 47G10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1060720-X
Keywords: Integral operators, eigenvalues, singular numbers
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society