Let <i>φ</i> be a self-map of <b>B</b><sub>2</sub>, the unit ball in <b>C</b><sup>2</sup>. We investigate the equation <i>C<sub>φ</sub>f</i>=<i>λf</i> where we define <i>C<sub>φ</sub>f </i>: -<i>f◦φ</i>, with <i>f a</i> function in the Drury Arves on Space. After imposing conditions to keep <i>C<sub>φ</sub></i> bounded and well-behaved, we solve the equation <i>C<sub>φ</sub>f - λf </i>and determine the spectrum <i>σ</i>(<i>C<sub>φ</sub></i>) in the case where there is no interior fixed point and boundary fixed point without multiplicity. We then investigate the existence of one-parameter semigroups for such maps and discuss some generalizations.
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/12360935 |
| Date | 15 June 2020 |
| Creators | Michael R Pilla (8882636) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/Spectra_of_Composition_Operators_on_the_Unit_Ball_in_Two_Complex_Variables/12360935 |
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