On algebras with convolution structures for Laguerre polynomials
HTML articles powered by AMS MathViewer
- by Yūichi Kanjin PDF
- Trans. Amer. Math. Soc. 295 (1986), 783-794 Request permission
Abstract:
In this paper we treat the convolution algebra connected with Laguerre polynomials which was constructed by Askey and Gasper [1]. For this algebra, we study the maximal ideal space, Wiener’s general Tauberian theorem, spectral synthesis and Helson sets. We also study Sidon sets and idempotent measures for the algebras with dual convolution structures.References
- Richard Askey and George Gasper, Convolution structures for Laguerre polynomials, J. Analyse Math. 31 (1977), 48–68. MR 486692, DOI 10.1007/BF02813297
- Charles F. Dunkl, Operators and harmonic analysis on the sphere, Trans. Amer. Math. Soc. 125 (1966), 250–263. MR 203371, DOI 10.1090/S0002-9947-1966-0203371-9 A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions, vol. II, McGraw-Hill, New York, 1953.
- George Gasper, Banach algebras for Jacobi series and positivity of a kernel, Ann. of Math. (2) 95 (1972), 261–280. MR 310536, DOI 10.2307/1970800
- E. Görlich and C. Markett, A convolution structure for Laguerre series, Nederl. Akad. Wetensch. Indag. Math. 44 (1982), no. 2, 161–171. MR 662652 S. Igari, Certain Banach algebras and Jacobi polynomials, Lecture Note Ser. No. 110, RIMS, Kyoto, 1971, pp. 36-46. (Japanese)
- Satoru Igari and Yoshikazu Uno, Banach algebra related to the Jacobi polynomials, Tohoku Math. J. (2) 21 (1969), 668–673; correction, ibid. (2) 22 (1970), 142. MR 433123, DOI 10.2748/tmj/1178242910
- Jean-Pierre Kahane, Séries de Fourier absolument convergentes, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 50, Springer-Verlag, Berlin-New York, 1970 (French). MR 0275043
- Benjamin Muckenhoupt, Mean convergence of Hermite and Laguerre series. I, II, Trans. Amer. Math. Soc. 147 (1970), 419-431; ibid. 147 (1970), 433–460. MR 0256051, DOI 10.1090/S0002-9947-1970-0256051-9
- Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
- Alan Schwartz, The structure of the algebra of Hankel transforms and the algebra of Hankel-Stieltjes transforms, Canadian J. Math. 23 (1971), 236–246. MR 273312, DOI 10.4153/CJM-1971-023-x G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R.I., 1975. G. N. Watson, Another note in Laguerre polynomials, J. London Math. Soc. 14 (1939), 19-22.
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 295 (1986), 783-794
- MSC: Primary 43A32; Secondary 42C10, 43A45, 43A46
- DOI: https://doi.org/10.1090/S0002-9947-1986-0833709-3
- MathSciNet review: 833709