On extensions of the Mittag-Leffler theorem

Ewa Ligocka

Annales Polonici Mathematici (1998)

  • Volume: 68, Issue: 3, page 249-256
  • ISSN: 0066-2216

Abstract

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The classical Mittag-Leffler theorem on meromorphic functions is extended to the case of functions and hyperfunctions belonging to the kernels of linear partial differential operators with constant coefficients.

How to cite

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Ewa Ligocka. "On extensions of the Mittag-Leffler theorem." Annales Polonici Mathematici 68.3 (1998): 249-256. <http://eudml.org/doc/270451>.

@article{EwaLigocka1998,
abstract = {The classical Mittag-Leffler theorem on meromorphic functions is extended to the case of functions and hyperfunctions belonging to the kernels of linear partial differential operators with constant coefficients.},
author = {Ewa Ligocka},
journal = {Annales Polonici Mathematici},
keywords = {hyperfunction; Laurent expansion; elliptic; polyharmonic; hypoelliptic; P-convex for supports; harmonic and polyharmonic function},
language = {eng},
number = {3},
pages = {249-256},
title = {On extensions of the Mittag-Leffler theorem},
url = {http://eudml.org/doc/270451},
volume = {68},
year = {1998},
}

TY - JOUR
AU - Ewa Ligocka
TI - On extensions of the Mittag-Leffler theorem
JO - Annales Polonici Mathematici
PY - 1998
VL - 68
IS - 3
SP - 249
EP - 256
AB - The classical Mittag-Leffler theorem on meromorphic functions is extended to the case of functions and hyperfunctions belonging to the kernels of linear partial differential operators with constant coefficients.
LA - eng
KW - hyperfunction; Laurent expansion; elliptic; polyharmonic; hypoelliptic; P-convex for supports; harmonic and polyharmonic function
UR - http://eudml.org/doc/270451
ER -

References

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  1. [1] N. Aronszajn, T. Creese and L. Lipkin, Polyharmonic Functions, Clarendon Press, Oxford, 1983. 
  2. [2] S. Axler, P. Bourdon and W. Ramey, Harmonic Function Theory, Springer, 1992. Zbl0765.31001
  3. [3] M. Brelot, Eléments de la théorie classique du potentiel, 2-ème éd., Paris, 1961. 
  4. [4] S. Y. Chung, D. Kim and J. R. Lee, Generalized Bôcher's theorem, J. Math. Anal. Appl. 188 (1994), 341-345. Zbl0818.31004
  5. [5] S. J. Gardiner, Harmonic Approximation, London Math. Soc. Lecture Note Ser. 221, Cambridge Univ. Press, 1995. Zbl0826.31002
  6. [6] R. Harvey and J. C. Polking, A Laurent expansion for solutions to elliptic equations, Trans. Amer. Math. Soc. 180 (1973), 407-413. Zbl0285.35024
  7. [7] L. Hörmander, The Analysis of Linear Partial Differential Operators I, II, Springer, 1983. Zbl0521.35002
  8. [8] V. P. Palamodov, Linear Differential Operators with Constant Coefficients, Nauka, Moscow, 1967 (in Russian). Zbl0191.43401
  9. [9] P. Schapira, Théorie des Hyperfonctions, Lecture Notes in Math. 126, Springer, 1970. Zbl0201.44805
  10. [10] N. N. Tarkhanov, Laurent expansions and local properties of solutions of elliptic systems, Sibirsk. Mat. Zh. 29 (6) (1988), 124-134 (in Russian). 
  11. [11] N. N. Tarkhanov, Laurent Series for Solutions of Elliptic Equations, Nauka, Novosibirsk, 1991 (in Russian). Zbl0743.35021
  12. [12] N. N. Tarkhanov, The Analysis of Solutions of Elliptic Equations, Kluwer, Dordrecht, 1997. Zbl0877.35002
  13. [13] M. Wachman, Generalized Laurent series for singular solutions of elliptic partial differential equations, Proc. Amer. Math. Soc. 15 (1964), 101-108. Zbl0145.14503

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