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

• Autorzy: Ewa Ligocka
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

harmonic functions; harmonic polynomials; spherical harmonics; conjugate harmonic functions

Kategorie tematyczne

• 31B05: Harmonic, subharmonic, superharmonic functions
• 42C15: General harmonic expansions, frames

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1999
• Tom: 71
• Numer: 2
• Strony: 151-160

Daty

wydano

1999

otrzymano

1998-02-12

Twórcy

autor

Ewa Ligocka

• Department of Mathematics, Informatics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

• [1] N. Aronszajn, T. Creese and L. Lipkin, Polyharmonic Functions, Clarendon Press, Oxford, 1985.
• [2] S. Axler, P. Bourdon and W. Ramey, Harmonic Function Theory, Springer, 1992.
• [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.
• [4] J. Delsarte, Une extension nouvelle de la théorie des fonctions presque-périodiques de Bohr, Acta Math. 69 (1938), 259-317.
• [5] W. K. Hayman, Power series expansions for harmonic functions, Bull. London Math. Soc. 2 (1970), 152-158.
• [6] J. L. Lions, Opérateurs de Delsarte et problèmes mixtes, Bull. Soc. Math. France 84 (1956), 9-95.
• [7] B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17-92.
• [8] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.
• [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.
• [10] A. Weinstein, On a singular differential operator, Ann. Mat. Pura Appl. 49 (1960), 359-365.
• [11] R. Z. Yeh, Analysis and applications of holomorphic functions in higher dimensions, Trans. Amer. Math. Soc. 345 (1994), 151-177.