Almost everywhere convergence of Laguerre series

• Autorzy: Chang-Pao Chen , Chin-Cheng Lin
• Języki publikacji: EN

Abstrakty

EN

Let $a ∈ ℤ^+$ and $f ∈ L^p (ℝ^+), 1 ≤ p ≤ ∞ $. Denote by $c_j$ the inner product of f and the Laguerre function $ℒ^a_j$. We prove that if ${c_j}$ satisfies $lim_{λ↓1} \overline lim_{n→∞} ∑_{n

Słowa kluczowe

EN

almost everywhere convergence; Cesàro means; Laguerre polynomials; Riesz means

Kategorie tematyczne

• 42C15: General harmonic expansions, frames
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 109
• Numer: 3
• Strony: 291-301

Daty

wydano

1994

otrzymano

1993-08-12

Twórcy

autor

Chang-Pao Chen

• Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China

autor

Chin-Cheng Lin

• Department of Mathematics, National Central University, Chung-Li, Taiwan 32054, Republic of China

Bibliografia

• [1] R. Askey and S. Wainger, Mean convergence of expansions in Laguerre and Hermite series, Amer. J. Math. 87 (1965), 695-708.
• [2] C.-P. Chen, $L^1$-convergence of Fourier series, J. Austral. Math. Soc. Ser. A 41 (1986), 376-390.
• [3] C.-P. Chen, Pointwise convergence of trigonometric series, ibid. 43 (1987), 291-300.
• [4] J. Długosz, Almost everywhere convergence of some summability methods for Laguerre series, Studia Math. 82 (1985), 199-209.
• [5] G. H. Hardy, Divergent Series, Oxford Univ. Press, London, 1973.
• [6] B. Muckenhoupt, Poisson integrals for Hermite and Laguerre expansions, Trans. Amer. Math. Soc. 139 (1969), 231-242.
• [7] B. Muckenhoupt, Mean convergence of Hermite and Laguerre series I, ibid. 147 (1970), 419-431.
• [8] B. Muckenhoupt, Mean convergence of Hermite and Laguerre series II, ibid. 433-460.
• [9] G. Sansone, Orthogonal Functions, Yale Univ. Press, New Haven, Conn., 1959.
• [10] K. Stempak, Mean summability methods for Laguerre series, Trans. Amer. Math. Soc. 322 (1990), 671-690.
• [11] K. Stempak, Almost everywhere summability of Laguerre series, Studia Math. 100 (1991), 129-147.
• [12] K. Stempak, Almost everywhere summability of Laguerre series II, ibid. 103 (1992), 317-327.
• [13] G. Szegö, Orthogonal Polynomials, 3rd ed., Amer. Math. Soc., Providence, R.I., 1974.