FRAME BESSELIAN-g DI RUANG HILBERT

NUR HIDAYATIN, Dr. ATOK ZULIJANTO, M.Si

2015 | Tesis | S2 Matematika

Di dalam tesis ini dibahas tentang frame Besselian-g di ruang Hilbert yang merupakan generalisasi dari frame Besselian di ruang Hilbert. Terlebih dahulu diberikan teori tentang frame, basis riesz, dan frame Besselian beserta sifat-sifatnya serta hubungan antara frame, basis Riesz dan frame Besselian di ruang Hilbert. Selanjutnya dibahas sifat-sifat frame Besselian-g di ruang Hilbert serta hubungan frame Besselian-g dengan frame Besselian di ruang Hilbert dan hubungan frame Besselian-g dengan frame-g di ruang Hilbert.

In this thesis we study on g-Besselian frames in Hilbert spaces as a generalization of Besselian frames in Hilbert spaces. First, we give the concepts and the properties of a frame, a Riesz basis, and a Besselian frame, and the relations between a frame, a Riesz basis, and a Besselian frame in Hilbert spaces. Furthermore we discuss about the properties of g-Besselian frames in Hilbert spaces. Finally, we consider the relations between a g-Besselian frame and a Besselian frame, and a g-Besselian frame and a g-frame in Hilbert spaces.

Kata Kunci : frame, frame Besselian, frame-g, frame Besselian-g