Exponentials Form a Basis of Discrete Holomorphic Functions on a Compact

Christian Mercat

Bulletin de la Société Mathématique de France (2004)

  • Volume: 132, Issue: 2, page 305-326
  • ISSN: 0037-9484

Abstract

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We show that discrete exponentials form a basis of discrete holomorphic functions on a finite critical map. On a combinatorially convex set, the discrete polynomials form a basis as well.

How to cite

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Mercat, Christian. "Exponentials Form a Basis of Discrete Holomorphic Functions on a Compact." Bulletin de la Société Mathématique de France 132.2 (2004): 305-326. <http://eudml.org/doc/272342>.

@article{Mercat2004,
abstract = {We show that discrete exponentials form a basis of discrete holomorphic functions on a finite critical map. On a combinatorially convex set, the discrete polynomials form a basis as well.},
author = {Mercat, Christian},
journal = {Bulletin de la Société Mathématique de France},
keywords = {discrete holomorphic functions; discrete analytic functions; monodriffic functions; exponentials},
language = {eng},
number = {2},
pages = {305-326},
publisher = {Société mathématique de France},
title = {Exponentials Form a Basis of Discrete Holomorphic Functions on a Compact},
url = {http://eudml.org/doc/272342},
volume = {132},
year = {2004},
}

TY - JOUR
AU - Mercat, Christian
TI - Exponentials Form a Basis of Discrete Holomorphic Functions on a Compact
JO - Bulletin de la Société Mathématique de France
PY - 2004
PB - Société mathématique de France
VL - 132
IS - 2
SP - 305
EP - 326
AB - We show that discrete exponentials form a basis of discrete holomorphic functions on a finite critical map. On a combinatorially convex set, the discrete polynomials form a basis as well.
LA - eng
KW - discrete holomorphic functions; discrete analytic functions; monodriffic functions; exponentials
UR - http://eudml.org/doc/272342
ER -

References

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  10. [10] R. Kenyon – « The Laplacian and Dirac operators on critical planar graphs », Invent. Math. 150 (2002), no. 2, p. 409–439, http://arXiv.org/abs/math-ph/0202018. Zbl1038.58037MR1933589
  11. [11] C. Mercat – « Discrete Period Matrices and Related Topics », http://arXiv.org/abs/math-ph/0111043. 
  12. [12] —, « Discrete Polynomials and Discrete Holomorphic Approximation », http://arXiv.org/abs/math-ph/0206041. 
  13. [13] —, « Discrete Riemann surfaces and the Ising model », Comm. Math. Phys. 218 (2001), no. 1, p. 177–216. Zbl1043.82005MR1824204

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