El mètode de Phragmén-Lindelöf i aplicacions: teorema de Riesz-Thorin i d’incertesa de Hardy
| Autor: | Palacios Torrell, Roger |
|---|---|
| Přispěvatelé: | Cascante, Ma. Carme (Maria Carme) |
| Jazyk: | Catalan; Valencian |
| Rok vydání: | 2023 |
| Předmět: | |
| Popis: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Ma. Carme Cascante [en] The Maximum Modulus Principle, which is one of the most important results in complex analysis, states that a holomorphic function defined on a bounded domain of $\mathbb{C}$, takes its maximum value at some point from the domain's boundary. Hence, the objective of this work is to introduce and apply the Phragmén-Lindelöf method in order to extend the conclusions given by the Maximum Modulus Principle to unbounded domains. Furthermore, this method will be used to see some applications such as: the Hadamard Three Lines Theorem, which provides good enough bounds for holomorphic functions on vertical strips; the Riesz-Thorin Interpolation Theorem, which establishes that a linear operator between measurable function spaces is bound in certain Lebesgue spaces $L^p$; and the Hardy's Uncertainty Principle, which claims that a measurable function and its Fourier transform cannot simultaneously have compact support, unless they both are identically zero. |
| Databáze: | OpenAIRE |
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