Stein-Weiss gradients
| Autor: | Malý, Marek |
|---|---|
| Přispěvatelé: | Lávička, Roman, Souček, Vladimír |
| Jazyk: | čeština |
| Rok vydání: | 2020 |
| Předmět: |
invariant differental operators
Cauchy-Riemann equations spin grupa Clifford algebra invariantní diferenciální operátory Hodge-de Rhamův systém diferenciálních rovnic the~Dirac operator Cliffordova algebra spin group Diracův operátor Cauchy-Riemannovy podmínky Hodge-de~Rham system of differential equations |
| Popis: | In this bachelor thesis, we describe the construction of rotation invariant differential operators of first order on the Euklidean space Rn given by E. Stein and G. Weiss. For this construction we show how to find an irreducible decomposition of a tensor product of re- presentations of group Spin(n) into irreducible subrepresetations. We shall also prove the rotation invariance of the gradient operator. Then we apply the Stein-Weiss construction to produce some of well-known differential operators. Namely, we construct the Dirac operator in Rn and Hodge-de Rham system of differential equations using this method. 1 |
| Databáze: | OpenAIRE |
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