Locally Convex Topological Vector Spaces

Daniel Alpay
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Daniel Alpay: Ben-Gurion University of the Negev

Chapter Chapter 5 in An Advanced Complex Analysis Problem Book, 2015, pp 249-283 from Springer

Abstract: Abstract Locally convex topological vector spaces form an important class of topological spaces. We have already seen some examples in the previous chapter. This chapter is motivated in part by the study of the space of functions analytic in a given open set and of its dual, and by the study of spaces of test functions and of distributions (for instance the Schwartz space and the space of tempered distributions). For general references on topological vector spaces we refer to [146, 251, 307], and to the book [202] for counterexamples in the theory.

Keywords: Hilbert Space; Vector Space; Compact Subset; Normed Space; Topological Vector Space (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-16059-7_5

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