On the Laguerre calculus of left-invariant convolution (pseudo-differential) operators on the Heisenberg group

Peter C. Greiner

Séminaire Équations aux dérivées partielles (Polytechnique) (1980-1981)

  • page 1-39

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Greiner, Peter C.. "On the Laguerre calculus of left-invariant convolution (pseudo-differential) operators on the Heisenberg group." Séminaire Équations aux dérivées partielles (Polytechnique) (1980-1981): 1-39. <http://eudml.org/doc/111771>.

@article{Greiner1980-1981,
author = {Greiner, Peter C.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {Laguerre matrix; generalized Laguerre functions; Mikhlin-Calderon-Zygmund calculus},
language = {eng},
pages = {1-39},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {On the Laguerre calculus of left-invariant convolution (pseudo-differential) operators on the Heisenberg group},
url = {http://eudml.org/doc/111771},
year = {1980-1981},
}

TY - JOUR
AU - Greiner, Peter C.
TI - On the Laguerre calculus of left-invariant convolution (pseudo-differential) operators on the Heisenberg group
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1980-1981
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 39
LA - eng
KW - Laguerre matrix; generalized Laguerre functions; Mikhlin-Calderon-Zygmund calculus
UR - http://eudml.org/doc/111771
ER -

References

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  1. [1] Beals, R.W. and Greiner, P.C., "Non-elliptic differential operators of type □b", (in preparation). 
  2. [2] Folland, G.B., "A fundamental solution for a subelliptic operator", Bull. Amer. Math. Soc.79 (1973), pp . 373 -376. Zbl0256.35020MR315267
  3. [3] Folland, G.B. and Stein, E.M., "Estimates for the ∂ b - complex and analysis on the Heisenberg group", Comm. Pure Appl. Math.27 (1974), pp. 429 - 522. Zbl0293.35012
  4. [4] Geller, D., "Fourier analysis on the Heisenberg group. I. Schwartz space", J. Func. Analysis36 (1980), pp. 205-254. Zbl0433.43008MR569254
  5. [5] Geller, D., "Local solvability and homogeneous distributions on the Heisenberg group", Comm . PDE, 5 (5) (1980), pp. 475-560. Zbl0488.22020MR571049
  6. [6] Greiner, P.C., Kohn, J.J. and Stein, E.M., "Necessary and sufficient conditions for the solvability of the Lewy equation", Proc. Nat. Acad. of Sciences, U.S.A., 72 (1975), pp. 3287-3289. Zbl0308.35017MR380142
  7. [7] Greiner, P.C. and Stein, E.M., "Estimates for the ∂-Neumann problem ", Math. Notes Series, n° 19, Princeton, Univ. Press, Princeton, N.J.1977. Zbl0354.35002
  8. [8] Greiner, P.C., and Stein, E.M., "On the solvability of some differential operators of type □ b", Proc. of the Seminar on Several Complex Variables, Cortona, Italy, 1976- 1977, pp. 106-165. Zbl0434.35007
  9. [9] Koranyi, A. and Vagi, S., "Singular integrals in homogeneous spaces and some problems of classical analysis", Ann. Scuola Norm. Sup. Pisa25 (1971), pp. 575-648. Zbl0291.43014MR463513
  10. [10] Lewy, H., "An example of a smooth linear partial differential equation without solution", Ann. of Math., 66 (1957), pp. 155-158. Zbl0078.08104MR88629
  11. [11] Mauceri, G., "The Weyl transform and bounded operators on Lp (lRn)", Report n° 54 of the Math. Inst. of the Univ. of Genova, 1980. 
  12. [12] Mikhlin, S.G., "Multidimensional singular integrals and integral equations", Pergamon Press, 1965. Zbl0129.07701MR185399
  13. [13] Nagel, A. and Stein, E.M., "Lectures on pseudo-differential operators", Math. Notes Series, n° 24, Princeton Univ. Press, Princeton, N.J.1979. Zbl0415.47025MR549321
  14. [14] Seeley, R.T., "Elliptic Singular Integral Equations", Amer. Math. Soc. Proc. Symp. Pure Math.10 (1967), pp. 308-315. Zbl0177.38603MR234107
  15. [15] Szegö, G., "Orthogonal polynomials", Amer. Math. Soc. Colloquium Publ., V. 23, Amer. Math. Soc., Providence, R.I., 1939. Zbl0023.21505

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