Paths, Integrals, Derivatives

John Mac Sheridan Nerney
Additional contact information
John Mac Sheridan Nerney: Mathematics

Chapter Chapter 3 in An Introduction to Analytic Functions, 2020, pp 17-23 from Springer

Abstract: Abstract A simple subdivision Simple subdivision of an interval [a, b] is a nondecreasing sequence { t p } p = 0 n $$\{t_p\}_{p=0}^n$$ with values in [a, b] such that t 0 = a and t n = b. If [a, b] is in the domain of a complex function x, then x is of bounded variation on [a, b] Complex function of bounded variation if there is a number v such that for every simple subdivision { t p } p = 0 n $$\{t_p\}_{p=0}^n$$ , we have ∑ p = 1 n | x ( t p ) − x ( t p − 1 ) | ≤ v $$\sum _{p=1}^n|x(t_p)-x(t_{p-1})|\leq v$$ . The least upper bound of such v is called the total variation of x on [a, b] Complex function total variation of and denoted by ∫ a b | d x | $$\int _a^b|dx|$$ ∫ a b | d x | $$\int _a^b\vert dx\rvert $$ .

Date: 2020
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-42085-7_4

Ordering information: This item can be ordered from
http://www.springer.com/9783030420857

DOI: 10.1007/978-3-030-42085-7_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().