Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Generalized absolute convergence of Fourier-Jacobi expansions. |
| Συγγραφείς: |
Tyr, Othman1 (AUTHOR) otywac@hotmail.fr, Dades, Abdelaali2 (AUTHOR) |
| Πηγή: |
Integral Transforms & Special Functions. Aug2026, Vol. 37 Issue 8, p690-708. 19p. |
| Θεματικοί όροι: |
*Jacobi polynomials, *Fourier analysis, *Smoothness of functions, *Signal convolution |
| Περίληψη: |
This paper provides sufficient conditions for the finiteness of the series \[ \sum_{k=0}^{\infty}\gamma_{k}|a_{k}(f)|^{r}\theta_{k}, \quad 0 ∑ k = 0 ∞ γ k | a k (f) | r θ k , 0 < r < 2 , where $ a_{k}(f) $ a k (f) are the Jacobi coefficients, $ \theta _{k} $ θ k is the Jacobi weight and $ \{\gamma _{k}\} $ { γ k } is a given sequence of non-negative real numbers satisfying a mild assumption. These sufficient conditions are formulated in terms of the modulus of smoothness of arbitrary order. These results are inspired by a result obtained by Gogoladze and Meskhia on the absolute convergence of the Fourier trigonometric series, which generalizes well-known results by Bernstein and Szász. Some results concerning the absolute convergence of the Jacobi convolution are also given. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: |
Academic Search Index |