38
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Algebraicity in the Dirichlet problem in the plane with rational data

, , &
Pages 235-244 | Received 30 Sep 2006, Published online: 19 Oct 2007

References

  • Bell , SR , Ebenfelt , P , Khavinson , D and Shapiro , HS . On the classical Dirichlet problem in the plane with rational data . Journal d'Analyse Mathématique , (To appear)
  • Shapiro , HS . 1989 . An algebraic theorem of E. Fischer, and the holomorphic Goursat problem . Bulletin of the London Mathematical Society , 21 : 513 – 537 .
  • Khavinson , D and Shapiro , HS . 1992 . Dirichlet's problem when the data is an entire function . Bulletin of the London Mathematical Society , 24 : 456 – 468 .
  • Render , H . 2005 . Real Bargmann spaces, Fischer pairs and sets of uniqueness for polyharmonic functions . (Preprint)
  • Ebenfelt , P , Khavinson , D and Shapiro , HS . 2005 . “ Algebraic aspects of the Dirichlet problem ” . In Quadrature Domains and Their Applications Vol. 156 , 151 – 172 . Operator Theory: Advances and Applications
  • Ebenfelt , P . 1992 . Singularities encountered by the analytic continuation of solutions to Dirichlet's problem . Complex Variables, Theory and Application , 20 : 75 – 92 .
  • Ebenfelt , P and Viscardi , M . 2005 . On the solution of the Dirichlet problem with rational boundary data . Computational Methods and Function Theory , 5 : 445 – 457 .
  • Ebenfelt , P and Viscardi , M . 2006 . An explicit solution to the dirichlet problem with rational holomorphic data in terms of a riemann mapping . (Preprint)
  • Bell , SR . 1995 . Complexity of the classical kernel functions of potential theory . Indiana University Mathematics Journal , 44 : 1337 – 1369 .
  • Bell , SR . 1992 . The Cauchy Transform, Potential Theory, and Conformal Mapping , Boca Raton : CRC Press .
  • Davis , P . 1974 . “ Carus Mathematical Monographs ” . In The Schwarz Function and its Applications , Vol. 17 , Buffalo , NY : Mathematical Association of America .
  • Shapiro , HS . 1992 . The Schwarz Function and its Generalization to Higher Dimensions , New York : Wiley-Interscience .
  • Hansen , LJ and Shapiro , HS . 1994 . Functional equations and harmonic extensions . Complex Variables, Theory and Application , 24 : 121 – 129 .
  • Khavinson , SYa . 1997 . “ Best approximation by linear superpositions (approximate nomography) ” . Vol. 159 , Providence , RI : American Mathematical Society . Translated from the Russian manuscript by D. Khavinson. Translations of Mathematical Monographs

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.