تقرير
Operator Diagonalizations of Multiplier Sequences
| العنوان: | Operator Diagonalizations of Multiplier Sequences |
|---|---|
| المؤلفون: | Bates, Robert D. |
| سنة النشر: | 2014 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Complex Variables |
| الوصف: | We consider hyperbolicity preserving operators with respect to a new linear operator representation on $\mathbb{R}[x]$. In essence, we demonstrate that every Hermite and Laguerre multiplier sequence can be diagonalized into a sum of hyperbolicity preserving operators, where each of the summands forms a classical multiplier sequence. Interestingly, this does not work for other orthogonal bases; for example, this property fails for the Legendre basis. We establish many new formulas concerning the $Q_k$'s of Peetre's 1959 differential representation for linear operators in the specific case of Hermite and Laguerre diagonal differential operators. Additionally, we provide a new algebraic characterization of the Hermite multiplier sequences and also extend a recent result of T. Forg\'acs and A. Piotrowski on hyperbolicity properties of the polynomial coefficients in hyperbolicity preserving Hermite diagonal differential operators. Comment: 23 pages, Made more organized |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1404.1631 |
| رقم الأكسشن: | edsarx.1404.1631 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |