A one parameter family of Volterra-type operators
| Autor: | Battistoni, Francesco, Molteni, Giuseppe |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | For every $\alpha \in (0,+\infty)$ and $p,q \in (1,+\infty)$ let $T_\alpha$ be the operator $L^p[0,1]\to L^q[0,1]$ defined via the equality $(T_\alpha f)(x) := \int_0^{x^\alpha} f(y) d y$. We study the norms of $T_\alpha$ for every $p$, $q$. In the case $p=q$ we further study its spectrum, point spectrum, eigenfunctions, and the norms of its iterates. Moreover, for the case $p=q=2$ we determine the point spectrum and eigenfunctions for $T^*_\alpha T_\alpha$, where $T^*_\alpha$ is the adjoint operator. Comment: To appear in Rend. Circ. Mat. Palermo (2) |
| Databáze: | arXiv |
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