Weighted composition operators |
Posted on:2006-01-14 | Degree:Ph.D | Type:Thesis |
University:Purdue University | Candidate:Gunatillake, Gajath K | Full Text:PDF |
GTID:2450390005498984 | Subject:Mathematics |
Abstract/Summary: | |
This thesis contains some results on weighted composition operators on weighted Hardy spaces of the open unit disk D of the complex plane. If psi is an analytic map on the open unit disk and ϕ an analytic map from the open unit disk into itself, the weighted composition operator Cpsi,ϕ is defined by Cpsi,ϕ( f)(z) = psi(z)f(ϕ( z)). These operators come up naturally. Back in 1964 Forelli showed that every isometry on Hp for 1 < p < infinity and p ≠ 2 is a weighted composition operator [4]. Weighted composition operators have also appeared in recent work of Clifford and Dabkowski [1] and also Shapiro and Smith [8].;Chapter 1 contains definitions and some well known results. The second chapter contains some results on the interaction between psi and ϕ that is necessary for the boundedness of the operator. The compact operators of this kind are discussed in Chapter 3. A few theorems are given that enable us to construct interesting compact weighted composition operators. The spectrum of a compact operator is also computed. Spectrum of some non-compact operators are discussed in Chapter 4. The last chapter discussus Hilbert-Schmidt operators. |
Keywords/Search Tags: | Operators, Weighted composition, Open unit disk, Chapter |
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