تقرير
A characterization of differential operators in the ring of complex polynomials
العنوان: | A characterization of differential operators in the ring of complex polynomials |
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المؤلفون: | Fechner, Włodzimierz, Gselmann, Eszter |
سنة النشر: | 2023 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Classical Analysis and ODEs, Primary: 47B92, Secondary: 13B25, 39B22, 47J05, 47A62, 47B38 |
الوصف: | The paper aims to provide a full characterization of all operators $T\colon \mathscr{P}(\mathbb{C}) \to \mathscr{P}(\mathbb{C})$ acting on the space of all complex polynomials that satisfy the Leibniz rule \[ T(f\cdot g)= T(f)\cdot g+f\cdot T(g) \] for all $f, g\in \mathscr{P}(\mathbb{C})$. We do not assume the linearity of $T$. As we will see, contrary to the well-known theorems for function spaces there are many other solutions here, not only differential operators. From our main result, we also derive two corollaries, showing that in some special cases operators that satisfy the Leibniz rule have some particular form. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2311.04671 |
رقم الأكسشن: | edsarx.2311.04671 |
قاعدة البيانات: | arXiv |
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