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Title: A Family of Banach Spaces Over ℝ∞
In T. L. Gill and W. W. Zachary, Functional Analysis and the Feynman Operator Calculus (Springer, New York, 2016), the topology of [Formula: see text] was replaced with a new topology and denoted by [Formula: see text]. This space was then used to construct Lebesgue measure on [Formula: see text] in a manner that is no more difficult than the same construction on [Formula: see text]. More important for us, a new class of separable Banach spaces [Formula: see text], [Formula: see text], for the HK-integrable functions, was introduced. These spaces also contain the [Formula: see text] spaces and the Schwartz space as continuous dense embeddings. This paper extends the work in T. L. Gill and W. W. Zachary, Functional Analysis and the Feynman Operator Calculus (Springer, New York, 2016) from [Formula: see text] to [Formula: see text].  more » « less
Award ID(s):
2016406 1928930
PAR ID:
10280589
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Proceedings of the Singapore National Academy of Science
Volume:
15
Issue:
01
ISSN:
2591-7226
Page Range / eLocation ID:
9 to 15
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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