Treść książki
Przejdź do opcji czytnikaPrzejdź do nawigacjiPrzejdź do informacjiPrzejdź do stopki
13
includesomeveryrecentresults–thistheoryisstillbeingdeveloped
asof2020.)
Contrarytothecustom,weincludedaflpreliminary”chapterat
theveryendofthebook.Itisnotachapterthatshouldberead,but
onlyconsultedifweusesomenotion,notationorconventionthereader
isnotfamiliarwith,andputtingitatthebeginningwouldmakethe
falseimpressionthatwewanteveryonetoactuallyreaditinfull.In
fact,itcanbetreatedasanappendixratherthananythingelse.We
alsopreparedtwoindices–oneisanalphabeticindexofnotionsand
names,andtheotherisasemi-alphabeticindexofsymbols(theflsemi”
prefixcomesfromthefactthattheirorderissometimesabitarbi-
trary–somesymbolssharethesameletters,somedonothavealetter
inthematall).
Acommonthemerunningthroughtheentirebookistheemphasis
putonexamples,applicationsandinterestingbutnotwidelyknown
results.Weincludedsomethingoutsidetheflusual”choiceoftopicsin
everychapter.Forexample,wehaveBessaga’sconversetotheBanach
contractionprinciple(Theorem2.1.11),adecompositionofanidentity
functionon
R
intoasumoftwoperiodicfunctions(Example4.1.22),
anestimationforthedifferencebetweentheintegralofaproductof
twofunctionsandtheproductoftheirintegrals(Theorem6.3.21),and
manyothers.Havingsuchawideselectionoftheoremsenabledus
alsotoshowcasetherichnessofproofmethodsinnonlinearanalysis.
Wewouldliketothankmanypeoplewhomadethisprojectfeasi-
ble.Ourfamilieswhohadtoputupwithourlongdiscussionsand
latenight(andearlymorning)writingsessionsareperhapsthemost
prominent,butwearealsoindebtedtoourcolleaguesProfessorPiotr
MaćkowiakandDoctorBartłomiejPrzybylskiforreadingthrough
partialearlierversionsandsharingtheirremarkswithus.During
writingthisbook,weusedvarioustoolswhichweregenerouslymade
freebytheirauthors–thefamousL
A
T
E
Xtypesettingsystem,T
E
XGyre
PagellaandEulerfontsandmany,manyothers.Ourworkwouldbe
muchmoredifficultifnotforthem.
Weworkedreally,reallyhardtomakesurethatalltheorems,lem-
mata,corollariesetc.aretrue,andtheirproofscorrect.Havingseen
I
