Hardy Spaces on Unit Disk and Nevanlinna-Pick's Interpolation Problem

Hembram, Pallab Kumar (2021) Hardy Spaces on Unit Disk and Nevanlinna-Pick's Interpolation Problem. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Pallab Kumar Hembram (16MS012)) 16MS012_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

My project works consist of two parts. In �rst part we describes the basics of the Hardy spaces. The Hardy space part includes the de�nition of Hardy Spaces, properties of Hardy space, F.Riesz factorization theorem, Fatou's theorem, Inner-Outer Factorization theorem, Hardy-Hilbert spaces. The second part describes the Nevanlinna-Pick's Interpolation problem. It includes Nevanlinna-Pick's Interpolation theorem based on Schur's algorithm, Nevanlinna parametrization of solution, and some possible geometrical interpretation of three point Nevanlinna-Pick's interpolation.

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