Thesis (Ph. D.)--Oregon State University, 1976. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.

Thesis (doctoral)--Georg-August-Universität zu Göttingen, 1920. / Vita. Includes bibliographical references (p. [53]-54).

Abstract of Thesis (Ph. D.)--University of Illinois, 1926. / Vita.

This thesis consists of two parts. In the first part, we study summability in left amenable semigroups. More explicitly, various summability methods defined by matrices are considered. Necessary and (or) sufficient conditions are given for matrices to be regular, almost regular, Schur, almost Schur, strongly regular and almost strongly regular, generalizing those of O. Toeplitz, J. P. King, J. Schur, G. G. Lorentz and P. Schaefer for the semigroup of additive positive integers. The theorems are of interest even for the semigroup of multiplicative positive integers. Let S be a topological semigroup which is amenable as a discrete semigroup. Denote by LUC(S) the set of bounded real-valued left uniformly continuous functions on S. It is shown by E. Granirer that if S is a separable topological group which is amenable as a discrete group and has a certain property (B) then LUC(S) has "many" left invariant means. In the second part of this thesis, we extend this result to certain topological subsemigroups of a topological group. In particular, we show that if S is a separable closed non-compact subsemigroup of a locally compact group which is amenable as a discrete semigroup then LUC(S) has "many" left invariant means. Finally, an example is given to show that this result cannot be extended to every topological semigroup. / Science, Faculty of / Mathematics, Department of / Graduate

It will be our purpose to study a generalized definition of sum of a series and the restrictions which must be placed upon it in order that it shall satisfy the generally accepted requirements of any generalized definition of sum of a series. We shall then proceed to investigate the possibilities of further generalizing this process.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Diss.--Stuttgart. / Vita. Bibliography: p. 86-88.

"The purpose of this paper is to study methods by which a value can be assigned to an infinite series. The reason for studying about these methods lies in the fact that infinite series often appear as the end result of a calculation or computation. A desire to obtain a usable end result leads us to the investigation of methods for evaluating infinite series"--Introduction. / "August, 1955." / Typescript. / Advisor: Howard E. Taylor, Professor Directing Paper. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Includes bibliographical references (leaf 40).

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