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Mercerian theorems via spectral theory

1977
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Pacific Journal of Mathematics
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Given a regular matrix A, Mercerian theorems are concerned with determining the real or complex values of a for which al + (1a)A is equivalent to convergence. For aΦl, the problem is equivalent to determining the resolvent set for A, or, determining the spectrum σ(A) of A, where σ(A) = {λ IA -λl is not invertible}. This paper treats the problem of determining the spectra of weighted mean methods; i.e., triangular matrices A = (a nk ) with a nkp k /P n , where p 0 > 0, Pn ^ 0, Σ&=o Pk ~ P n It

doi:10.2140/pjm.1977.73.63
fatcat:nqnky7ponbdehfqtow2xcdr4hy