Abstract
We introduce generalized Lipschitz classes
$\mbox{Lip}^M(\eta)$ and $\mbox{lip}^M(\eta)$ of functions associated with the canonical Sturm-Liouville operator
\[L^M:=\frac{\mbox{d}^2}{\mbox{d}x^2}+\left(\frac{A'(x)}{A(x)}-2i\frac{a}{b}x\right)\frac{\mbox{d}}{\mbox{d}x}
-\left(\frac{a^2}{b^2}x^2+i\frac{a}{b}x\frac{A'(x)}{A(x)}+i\frac{a}{b}\right),\]
where $A$ is a nonnegative function satisfying certain conditions;
and we prove two versions of Boas-type theorems for the canonical Sturm-Liouville transform $\mathscr{F}^M$.
An application to the canonical Sturm-Liouville multipliers is given.
Boas-type results for the canonical Fourier-Bessel transform and the canonical
Fourier-Jacobi transform are special cases of this work.
Key words: Canonical Sturm-Liouville transform, generalized Lipschitz classes, Boas-type theorems, special cases.
Full Text
Article Information
| Title | Boas-type theorems for the linear canonical Sturm-Liouville
transform |
| Source | Methods Funct. Anal. Topology, Vol. 31 (2025), no. 1, 56-69 |
| DOI | 10.31392/MFAT-npu26_1.2025.06 |
| Milestones | Received 13/01/2025; Revised 09/04/2025 |
| Copyright | The Author(s) 2025 (CC BY-SA) |
Authors Information
Fethi Soltani
Facult´e des Sciences de Tunis, Laboratoire d’Analyse Math´ematique et Applications LR11ES11, Universit´e de Tunis El Manar, Tunis 2092, Tunisia Ecole Nationale d’Ing´enieurs de Carthage, Universit´e de Carthage, Tunis 2035, Tunisia
Maher Aloui
Facult´e des Sciences de Tunis, Laboratoire d’Analyse Math´ematique et Applications LR11ES11, Universit´e de Tunis El Manar, Tunis 2092, Tunisia Ecole Nationale d’Ing´enieurs de Carthage, Universit´e de Carthage, Tunis 2035, Tunisia
Citation Example
Fethi Soltani and Maher Aloui, Boas-type theorems for the linear canonical Sturm-Liouville
transform, Methods Funct. Anal. Topology 31
(2025), no. 1, 56-69.
BibTex
@article {MFAT2099,
AUTHOR = {Fethi Soltani and Maher Aloui},
TITLE = {Boas-type theorems for the linear canonical Sturm-Liouville
transform},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {31},
YEAR = {2025},
NUMBER = {1},
PAGES = {56-69},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_1.2025.06},
URL = {https://mfat.imath.kiev.ua/article/?id=2099},
}
