Convolution structure of (generalized) hermite transforms

Hans-Jürgen Glaeske

Banach Center Publications (2000)

  • Volume: 53, Issue: 1, page 113-120
  • ISSN: 0137-6934

How to cite

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Glaeske, Hans-Jürgen. "Convolution structure of (generalized) hermite transforms." Banach Center Publications 53.1 (2000): 113-120. <http://eudml.org/doc/209067>.

@article{Glaeske2000,
author = {Glaeske, Hans-Jürgen},
journal = {Banach Center Publications},
keywords = {convolution structure; Hermite transform; Hermite polynomials},
language = {eng},
number = {1},
pages = {113-120},
title = {Convolution structure of (generalized) hermite transforms},
url = {http://eudml.org/doc/209067},
volume = {53},
year = {2000},
}

TY - JOUR
AU - Glaeske, Hans-Jürgen
TI - Convolution structure of (generalized) hermite transforms
JO - Banach Center Publications
PY - 2000
VL - 53
IS - 1
SP - 113
EP - 120
LA - eng
KW - convolution structure; Hermite transform; Hermite polynomials
UR - http://eudml.org/doc/209067
ER -

References

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  1. [1] T. S. Chihara, Generalized Hermite polynomials, Ph. D. Thesis Purdue Univ. (1955). 
  2. [2] T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon & Breach, New York, 1978. Zbl0389.33008
  3. [3] L. Debnath, Some operational properties of Hermite transform, Math. Vesnik 5 (20) (1968), 29-36. Zbl0155.44902
  4. [4] I. H. Dimovski and S. L. Kalla, Explicit convolution for Hermite transform, Math. Japonica 33 (1988), 345-351. Zbl0649.44001
  5. [5] H.-J. Glaeske, On a convolution structure of a generalized Hermite transformation, Serdica 9 (1983), 223-229. Zbl0528.44001
  6. [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. Zbl0593.44004
  7. [7] H.-J. Glaeske and M. Saigo, On a hybrid Laguerre-Fourier transform, Integral Transform Spec. Funct., to appear. Zbl0976.44011
  8. [8] E. Görlich and C. Markett, A convolution structure for Laguerre series, Indag. Math. (N.S.) 44 (1982), 161-171. Zbl0489.42030
  9. [9] A. M. Krall, Spectral analysis for the generalized Hermite polynomials, Trans. Amer. Math. Soc. 344 (1994), 155-172. Zbl0859.33009
  10. [10] C. Markett, Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8 (1982), 19-37. Zbl0515.42023
  11. [11] C. Markett, The product formula and convolution structure associated with the generalized Hermite polynomials, J. Approx. Theory 73 (1993), 199-217. Zbl0777.33001
  12. [12] G. Szegö, Orthogonal Polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ. 23, Providence R.I., 1975. 
  13. [13] G. W. Watson, Another note in Laguerre polynomials, J. London Math. Soc. 14 (1939), 19-22. Zbl0020.21805

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