On the Hartogs-type series for harmonic functions on Hartogs domains in ℝ n × ℝ m , m ≥ 2

Ewa Ligocka

Annales Polonici Mathematici (1999)

  • Volume: 71, Issue: 2, page 151-160
  • ISSN: 0066-2216

Abstract

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We study series expansions for harmonic functions analogous to Hartogs series for holomorphic functions. We apply them to study conjugate harmonic functions and the space of square integrable harmonic functions.

How to cite

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Ewa Ligocka. "On the Hartogs-type series for harmonic functions on Hartogs domains in $ℝ^n × ℝ^m$, m ≥ 2." Annales Polonici Mathematici 71.2 (1999): 151-160. <http://eudml.org/doc/262674>.

@article{EwaLigocka1999,
abstract = {We study series expansions for harmonic functions analogous to Hartogs series for holomorphic functions. We apply them to study conjugate harmonic functions and the space of square integrable harmonic functions.},
author = {Ewa Ligocka},
journal = {Annales Polonici Mathematici},
keywords = {harmonic functions; harmonic polynomials; spherical harmonics; conjugate harmonic functions; harmonic function; conjugate harmonic function},
language = {eng},
number = {2},
pages = {151-160},
title = {On the Hartogs-type series for harmonic functions on Hartogs domains in $ℝ^n × ℝ^m$, m ≥ 2},
url = {http://eudml.org/doc/262674},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Ewa Ligocka
TI - On the Hartogs-type series for harmonic functions on Hartogs domains in $ℝ^n × ℝ^m$, m ≥ 2
JO - Annales Polonici Mathematici
PY - 1999
VL - 71
IS - 2
SP - 151
EP - 160
AB - We study series expansions for harmonic functions analogous to Hartogs series for holomorphic functions. We apply them to study conjugate harmonic functions and the space of square integrable harmonic functions.
LA - eng
KW - harmonic functions; harmonic polynomials; spherical harmonics; conjugate harmonic functions; harmonic function; conjugate harmonic function
UR - http://eudml.org/doc/262674
ER -

References

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  1. [1] N. Aronszajn, T. Creese and L. Lipkin, Polyharmonic Functions, Clarendon Press, Oxford, 1985. 
  2. [2] S. Axler, P. Bourdon and W. Ramey, Harmonic Function Theory, Springer, 1992. Zbl0765.31001
  3. [3] Z. Ben Nahia and N. Ben Salem, Spherical harmonics and applications associated with the Weinstein operator, in: Potential Theory - ICPT 94 (Kouty, 1994), de Gruyter, Berlin, 1996, 233-241. Zbl0858.33008
  4. [4] J. Delsarte, Une extension nouvelle de la théorie des fonctions presque-périodiques de Bohr, Acta Math. 69 (1938), 259-317. Zbl0020.01902
  5. [5] W. K. Hayman, Power series expansions for harmonic functions, Bull. London Math. Soc. 2 (1970), 152-158. Zbl0201.43302
  6. [6] J. L. Lions, Opérateurs de Delsarte et problèmes mixtes, Bull. Soc. Math. France 84 (1956), 9-95. Zbl0075.10804
  7. [7] B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17-92. Zbl0139.29002
  8. [8] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. Zbl0207.13501
  9. [9] K. Trimèche, Transformation intégrale de Weyl et théorème de Paley-Wiener associés à un opérateur différentiel singulier sur (0,1), J. Math. Pures Appl. 60 (1981), 51-98. Zbl0416.44002
  10. [10] A. Weinstein, On a singular differential operator, Ann. Mat. Pura Appl. 49 (1960), 359-365. Zbl0094.06101
  11. [11] R. Z. Yeh, Analysis and applications of holomorphic functions in higher dimensions, Trans. Amer. Math. Soc. 345 (1994), 151-177. Zbl0808.30029

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