|
Título:
|
Eigenvalues of Integral-Operators with Positive Definite Kernels Satisfying Integrated Holder
|
|
Autores:
|
Cobos, Fernando ;
Kühn, Thomas
|
|
Tipo de documento:
|
texto impreso
|
|
Editorial:
|
Academic Press-Elsevier Science, 1990
|
|
Palabras clave:
|
Estado = Publicado
,
Materia = Ciencias: Matemáticas: Análisis numérico
,
Tipo = Artículo
|
|
Resumen:
|
For a compact metric space X let ? be a finite Borel measure on X. The authors investigate the asymptotic behavior of eigenvalues of integral operators on L2(X, ?). These integral operators are assumed to have a positive definite kernel which satisfies certain conditions of H¨older continuity. For the eigenvalues _n, n 2 N, which are counted according to their algebraic multiplicities and ordered with respect to decreasing absolute values, the main result of this paper consists of estimates _n = O(n?1(_n(X))_) for n ! 1. Here _n(X) represents the entropy numbers of X, and _ is the exponent in the H¨older continuity condition of the kernel. It is shown that in some respect this estimate is optimal. In the special case where X = _ RN is a bounded Borel set, the above estimate yields _n = O(n?_/N?1) for n ! 1. The article concludes with some non-trivial examples of compact metric spaces with regular entropy behavior.
|
