ON THE COMPLETENESS OF (F(N THETA)) AND A RECIPROCAL THEOREM FOR ABSOLUTELY CONVERGENT DIRICHLET SERIES

Date

1980

Journal Title

Journal ISSN

Volume Title

Publisher

ProQuest Dissertations & Theses

YU Faculty Profile

Abstract

One of the basic questions in approximation theory is: given a Banach space B, and S a subset of B, under what conditions will S be "rich" enough to approximate any element of B by a finite linear combination of elements of S. The most important result of this type pertains to the case where B is the Banach space of continuous functions on a finite interval with the supremum norm, and S is the set of monomials {l,x,x 2, ••• }. In this case the famous Weierstrass Theorem asserts that any element of B can be uniformly approximated by a finite linear combination of elements of S, that is any continuous function on a finite interval can be uniformly approximated by a polynomial. (from Introduction)

Description

Doctoral dissertation, PhD / YU only

Keywords

Mathematics.

Citation

GOODMAN, A. (1980). On The Completeness Of (f(n Theta)) And A Reciprocal Theorem For Absolutely Convergent Dirichlet Series (Order No. 8021258). Available from ProQuest Dissertations & Theses Global. (303080749). Retrieved from https://ezproxy.yu.edu/login?url=https://www.proquest.com/dissertations-theses/on-completeness-f-n-theta-reciprocal-theorem/docview/303080749/se-2