OPERATOR SUPERPOSISI PADA RUANG C(Ω) THE SUPERPOSITION OPERATOR IN THE SPACE C(Ω)

Novalin Calasin Huwaa, S.Pd, Dr.Supama,M.Si

2013 | Tesis | S2 Matematika

Dalam tesis ini dibahas ruang fungsi kontinu 􀜥􁈺Ω􁈻 dan sifat-sifatnya, beberapa sifat fungsi Caratheodory, serta operator superposisi pada ruang fungsi kontinu dan sifat-sifatnya. Operator superposisi yang dibahas meliputi operator superposisi dari 􀜥􁈺Ω􁈻 ke 􀜥􁈺Ω􁈻, dari 􀜥􁈺Ω􁈻 ke suatu ruang fungsi terukur 􀜵􁈺Ω􁈻, serta dari 􀜵􁈺Ω􁈻 ke 􀜥􁈺Ω􁈻. Eksistensi operator-operator superposisi tersebut dijamin oleh sifat kontinu dan sup-terukur fungsi f yang membangkitkan operator superposisi F, serta sifat konstan operator superposisi F. Sifat kontinu operator superposisi F dari 􀜥􁈺Ω􁈻 ke 􀜥􁈺Ω􁈻 dijamin oleh sifat kontinu fungsi f yang membangkitkannya.

In this thesis, we discuss about the space of continuous functions and its properties, some properties of Caratheodory function, and the superposition operators on space of continuous functions and its properties. The operator of superposition that we discuss include the superposition operator from the space of continuous functions into itself , the space of continuous functions into the space of the measurable functions and from the space of measurable functions into itself. The existence of superposition operators is guaranteed by continuity properties and sup-measurable function f which generating the superposition operator F, and the constant properties of the superposition operator F. The properties of continuity of the superposition operator F from space of continuous functions into itself is guaranteed by the properties of continuity of function f which is generated it.

Kata Kunci : Fungsi Kontinu, Ruang fungsi Kontinu, Operator Superposisi