The Annual Meeting in New York
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Hilbert space. In this paper the following theorem is proved: every one-parameter continuous group of unitary transformations in abstract Hilbert space possesses a generating infinitesimal transformation of the form iT, where T is an Hermitian symmetric operator which is maximal, and conversely. 15. Professor G. M. Robison: The consistency and equivalence of certain definitions of summability of divergent double series. This paper deals with definitions of summability of divergent double sequences which can be expressed by means of a linear transformation. Let xm,n be the given sequence. A new sequence ymtn is defined by the relation ym,n =Yl k-hi=im,n,k,iXk,h where the am,n,k,ïs form a set of constants defining the transformation, which we denote by (A ). If lim m,n+*>ym,n exists and equals X, we say tha t X is the generalized value of the sequence {xm<n) by the transformation (^4). This paper shows that all regular transformations of a certain class are consistent and gives a criterion for the equivalence of two regular definitions of summability. 168 AMERICAN MATHEMATICAL SOCIETY [Mar.-Apr., 16. Dr. Stefan Serghiesco: On the number of multiple common roots of a system of n equations. In several earlier papers, the author has introduced a new method for obtaining the number of simple common zeros of a set of n functions, and has given two new general formulas. In the present paper, the author extends this method of the case of multiple common zeros, stating the conditions of possibility with the corresponding formulas. 17. Dr. T. H. Rawles: On minimizing a function of two
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