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Preface
Thisbookisaddressedtotheworkingmathematicianwhowantsto
getanideaofthetheoryandapplicationsoffunctionsofbounded
variationwithoutgettingdrownedtoomuchintotechnicalities.Asthe
titlesuggests,thescopeismoreapplication-oriented,sothecentral
partisChapter4onexistence(andinpartuniqueness)resultsfornon-
linearintegralequationsofHammersteintype.Sincesuchequations
areintimatelyrelatedtoboundaryvalueproblems,ourresultsmay
simultaneouslyserveassourceofexistence(andinpartuniqueness)
resultsfornonlineardifferentialequations,subjecttovarioustypes
ofboundaryconditions.Asmallselectionofsuchproblemswillbe
giveninChapter5.
SinceweputthemainemphasisonChapter4,wewillgivecom-
pleteproofsinthatchapter.Inthepreviousthreechapterswewill
providethenecessarytheoreticalbackground.However,aswearenot
primarilyinterestedinthetheory,noproofswillbegiveninChap-
ters1–3forresultspublishedineasilyaccessiblejournals.Theonly
exceptionareveryrecentresults,mostlyobtainedbytheauthorsthem-
selves,whichhavenotbeenpublishedyet.
Theplanofthissurveyisasfollows.InChapter1wecollectthe
basicpropertiesofvariousspacesoffunctionsofboundedvariation,not
onlyinthesenseoftheclassicalJordanvariation,butalsoforthemore
generalWienervariation,Rieszvariation,andWatermanvariation.Givena
partition
P={t0
,
t1
,
...
,
tm−1
,
tm}
of
[
0,1
]
,where
m∈N
,weconsider
expressionsoftheform
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