کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4605136 | 1337549 | 2013 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An extension of Mercer theorem to matrix-valued measurable kernels
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: An extension of Mercer theorem to matrix-valued measurable kernels An extension of Mercer theorem to matrix-valued measurable kernels](/preview/png/4605136.png)
چکیده انگلیسی
We extend the classical Mercer theorem to reproducing kernel Hilbert spaces whose elements are functions from a measurable space X into Cn. Given a finite measure μ on X, we represent the reproducing kernel K as a convergent series in terms of the eigenfunctions of a suitable compact operator depending on K and μ. Our result holds under the mild assumption that K is measurable and the associated Hilbert space is separable. Furthermore, we show that X has a natural second countable topology with respect to which the eigenfunctions are continuous and such that the series representing K uniformly converges to K on compact subsets of X×X, provided that the support of μ is X.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied and Computational Harmonic Analysis - Volume 34, Issue 3, May 2013, Pages 339-351
Journal: Applied and Computational Harmonic Analysis - Volume 34, Issue 3, May 2013, Pages 339-351