except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.

Historical solutions to quadratics problems that do not rely on symbolic manipulation.

No abstract

No abstract

We show that for a class of operators which properly contains the normal operators on L2 , 1 "-' ■ 1 2"-' Wrf^a.e. iff 'j2T'f^a.e. 1=0 i=0 This theorem is used to give an alternate form of a theorem of Gaposhkin concerning the pointwise ergodic theorem for normal operators.