Ruang Fungsi Terintegralkan p Berbobot
DOI:
https://doi.org/10.15575/kubik.v3i1.2732Keywords:
Hasil kali dalam, ruang L^p (X), bobotAbstract
Pada artikel [2], telah berhasil didefinisikan suatu hasil kali dalam berbobot pada ruang L^p(X) untuk p>2. Oleh karena itu, inilah pertamakali kita pandang ruang L^p(X) untuk p>2 sebagai ruang hasil kali dalam. Dalam artikel ini, kita akan menunjukkan bahwa hasil kali dalam berbobot terdefinisi pada ruang yang lebih besar dari pada L^p(X) . Kita juga akan mempelajari hubungan ruang L^p(X) dengan ruang yang lebih besar tersebut dan menemukan banyak hasil yang menarik lainnya.
References
Kreyszig, E., “Introductory Functional Analysis with Applicationsâ€, John Wiley & Sons, New York, 1978.
Jakfar, M., Gunawan, H., dan Idris, M., “Hasil Kali Dalam Berbobot pada Ruang L^p (X)â€, Prosiding Semnastika 2015 Seminar Nasional Matematika dan Pendidikan Matematika, Unipress Unesa, Surabaya, 2015, pp. 298-304.
Jakfar, M., and Fuad, Y., “Generalized Fourier Transform On p-Integrable Function Spacesâ€, Proceedings IJCST The 1st International Joint Conference on Science and Technology, Universitas Pambangunan Nasional Veteran Jawa Timur, Surabaya.
Barberian, S.K., “Introduction to Hilbert Spacesâ€, Oxford Univ. Press., New York, 1961.
Stein, E.M., and Shakarchi, R., “Real Analisis: Measure Theory, Integration, and Hilbert Spacesâ€, Princeton Univ. Press., New Jerse, 2005.
A. Sahovic, “Generalized inner product on L^p (X), 1
B. Nath, “Topologies on generalized semi-inner product spaceâ€, Compositio Mathematica, 23: 309-316, 1971.
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