caa a22 4500 386385947 CHVBK 20180307112058.0 cr unu---uuuuu 161130e198901 xx s 000 0 eng 10.1017/S0305004100001481 doi S0305004100001481 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100001481 Oehring Charles Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, U.S.A. Spectral decay for definite kernels and functions [Elektronische Daten] [Charles Oehring] A classical theorem of Weyl [7] guarantees that the eigenvalues, ordered according to decreasing absolute values, of a symmetric kernel of class Cm (m ≥ 0) satisfy λn = o(n−m−½). Reade [5, 6] recently proved that if K is, in addition, positive definite, then λn = o(n−m−1;). He has also in [4] made similar improvements of classical spectral estimates for kernels of class Lip α. James Cochran pointed out to me that allied theorems for trigonometric Fourier coefficients seem to have been neglected in the literature. The trigonometric versions turn out to be elementary; nevertheless, in their conclusions concerning the decreasing rearrangement {f^*(n)} they generalize known results about the behaviour of monotone trigonometric transforms. Furthermore they suggest that the Cm hypothesis of Reade's theorem could be relaxed. Copyright © Cambridge Philosophical Society 1989 Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 161-163 0305-0041 105:1<161 1989 105 PSP https://doi.org/10.1017/S0305004100001481 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100001481 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Oehring Charles Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, U.S.A NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 161-163 0305-0041 105:1<161 1989 105 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge