Convolution structure of (generalized) hermite transforms

• Autorzy: Hans-Jürgen Glaeske
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2000
• Tom: 53
• Numer: 1
• Strony: 113-120

Daty

wydano

2000

Twórcy

autor

Hans-Jürgen Glaeske

• Fakultät für Mathematik, Friedrich-Schiller-Universität, D-07740 Jena, Germany

Bibliografia

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• [2] T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon & Breach, New York, 1978.
• [3] L. Debnath, Some operational properties of Hermite transform, Math. Vesnik 5 (20) (1968), 29-36.
• [4] I. H. Dimovski and S. L. Kalla, Explicit convolution for Hermite transform, Math. Japonica 33 (1988), 345-351.
• [5] H.-J. Glaeske, On a convolution structure of a generalized Hermite transformation, Serdica 9 (1983), 223-229.
• [6] H.-J. Glaeske, Die Faltungsstruktur Sturm-Liouvillescher Integraltransformationen, in: Mathematical Structures-Computational Mathematics - Mathematical Modelling, vol. 2, Publishing House of the Bulgarian Academy of Sciences, Sofia, 1984, 177-183.
• [7] H.-J. Glaeske and M. Saigo, On a hybrid Laguerre-Fourier transform, Integral Transform Spec. Funct., to appear.
• [8] E. Görlich and C. Markett, A convolution structure for Laguerre series, Indag. Math. (N.S.) 44 (1982), 161-171.
• [9] A. M. Krall, Spectral analysis for the generalized Hermite polynomials, Trans. Amer. Math. Soc. 344 (1994), 155-172.
• [10] C. Markett, Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8 (1982), 19-37.
• [11] C. Markett, The product formula and convolution structure associated with the generalized Hermite polynomials, J. Approx. Theory 73 (1993), 199-217.
• [12] G. Szegö, Orthogonal Polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ. 23, Providence R.I., 1975.
• [13] G. W. Watson, Another note in Laguerre polynomials, J. London Math. Soc. 14 (1939), 19-22.