MINIMIZATION OF NORM FUNCTION IN HILBERT SPACE Ha WITH CERTAIN CONSTRAINTS USING THE REPRODUCING KERNEL HILBERT SPACE

• Main Author: Agus Sutomo, Valantino
• Format: Theses
• Language: Indonesia
• Subjects: Matematika
• Online Access: https://digilib.itb.ac.id/gdl/view/33798
• Institution: Institut Teknologi Bandung

Reproducing kernel Hilbert space or abbreviated RKHS is a kernel in Hilbert space H, which has the nature to reproduce the function again. The nature of reproduce of that kernel is the inner product of the functions in the Hilbert space H with a kernel in the Hilbert space H, will produce that function again which evaluated at a certain point. A Hilbert space H is said reproducing kernel Hilbert space if there exists a reproducing kernel in Hilbert space H. A reproducing kernel Hilbert space has the single reproducing kernel of the Hilbert space H, furthermore that reproducing kernel is a positive and Hermitian matrix. The research on chapter 1 is focused on Banach spaces (normed space), Hilbert space (inner product space), the kernel, and the theory of reproducing kernel Hilbert space, also the examples of reproducing kernel Hilbert space. In chapter 2 will discuss a minimization of norm function in Hilbert space Ha with predetermined constraints. Hilbert space Ha is the inner product of the derivative function to a on L2(0;1). By using the Plancherel theorem and Fourier transformation, we define the norm of a function in a Hilbert space Ha. Finally the Propositions and theorems ultimately lead us in obtaining a single solution in the form of a linear combination of the reproducing kernel of Hilbert space Ha.