论文信息 - Eigenvalue distribution of Mercer‐like kernels

Eigenvalue distribution of Mercer‐like kernels

We study eigenvalues of positive definite kernels of L2 integral operators on arbitrary intervals. Assuming integrability and uniform continuity of the kernel on the diagonal, we show that the eigenvalue distribution is totally determined by the smoothness of the kernel together with its decay rate at infinity along the diagonal. Moreover, the rate of decay of eigenvalues depends on both these quantities in a symmetrical way. Our main result treats all possible orders of differentiability and all possible rates of decay of the kernel; the known optimal results for eigenvalue distribution of positive definite kernels in compact intervals are particular cases. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

J. Buescu | A. Paixao

[1] T. T. Kadota,et al. Term-by-term differentiability of Mercer’s expansion , 1967 .

[2] M. Kreĭn,et al. Introduction to the theory of linear nonselfadjoint operators , 1969 .

[3] M. Birman,et al. ESTIMATES OF SINGULAR NUMBERS OF INTEGRAL OPERATORS , 1977 .

[4] A. Pietsch. Eigenvalues of integral operators. I , 1980 .

[5] J. Reade. Eigenvalues of Positive Definite Kernels II , 1983 .

[6] Chung-Wei Ha. Eigenvalues of differentiable positive definite kernels , 1986 .

[7] J. Reade. Positive definite C P kernels , 1986 .

[8] Differentiable positive definite kernels and Lipschitz continuity , 1988 .

[9] J. Reade. Eigenvalues of smooth positive definite kernels , 1992, Proceedings of the Edinburgh Mathematical Society.

[10] Ching-Hua Chang,et al. On eigenvalues of differentiable positive definite kernels , 1999 .

[11] J. Buescu,et al. Positive-Definiteness, Integral Equations and Fourier Transforms , 2004 .

[12] J. Buescu. Positive integral operators in unbounded domains , 2004 .

[13] J. Buescu,et al. Eigenvalue Distribution of Positive Definite Kernels on Unbounded Domains , 2007 .