Christer Kiselman's research interests

My research interests include the following. (For a list of my papers, se my bibliography.)

Digital geometry

• 00-3. Digital Jordan curve theorems. Discrete Geometry for Computer Imagery. Gunilla Borgefors, Ingela Nyström, Gabriella Sanniti di Baja (Eds.), 9th International Conference, DGCI 2000, Uppsala, Sweden, December 13—15, 2000. Lecture Notes in Computer Science 1953. Springer, 2000. [Contains a new proof of Efim Khalimsky's digital Jordan curve theorem.] DVI - PS - PDF.
• 2004. Digital geometry and mathematical morphology. [Lecture notes to a course presented in 2004.]
• 10-1. Characterizing digital straightness by means of difference operators. In: Cris Luengo; Milan Gavrilovic (Eds.), Proceedings SSBA 2010. Symposium on Image Analysis, Uppsala, March 11—12, 2010, pp. 15–18. ISSN 1100-6641.
• 11-1. Characterizing digital straightness and digital convexity by means of difference operators. Mathematika 57 (2011), 355–380. Link to journal publication.

Mathematical morphology

• 07-2. Division of mappings between complete lattices. In: Mathematical Morphology and its Applications to Signal and Image Processing. Proceedings of the 8^th International Symposium on Mathematical Morphology, Rio de Janeiro, RJ, Brazil, October 10—13, 2007, pp. 27–38. G. J. F. Banon; J. Barrera; U. de Mendonça Braga-Neto, Eds. Saõ José dos Campos, SP: MCT/INPE.
• 10-2. Inverses and quotients of mappings between ordered sets. Image and Vision Computing 28 (2010), 1429–1442.

Discrete optimization

• 04-1. Convex functions on discrete sets. In: IWCIA 2004. R. Klette and J. Zunic (Eds.). Lecture Notes in Computer Science 3322 (2004), pp. 443–457.
• 08-1. Minima locaux, fonctions marginales et hyperplans séparants dans l'optimisation discrète. Comptes Rendus de l'Académie des Sciences Paris, Sér. I 346, 49–52.
• 04-1. Convex functions on discrete sets. In: IWCIA 2004. R. Klette and J. Zunic (Eds.). Lecture Notes in Computer Science 3322 (2004), pp. 443–457.
• 10-3. Local minima, marginal functions, and separating hyperplanes in discrete optimization. In: Rajendra Bhatia (Ed.), Abstracts: Short communications; Posters. International Congress of Mathematicians, Hyderabad, August 19–27, 2010, pp. 572–573.
• 10-4. Christer O. Kiselman; Shiva Samieinia, Convexity of marginal functions in the discrete case. In: Shiva Samieinia (2010), Digital Geometry, Combinatorics, and Discrete Optimization, published on 2010-12-15. PhD Thesis defended at Stockhom University on 2011-01-21.

Convexity theory

• 92-2. Regularity classes for operations in convexity theory. Kodai Mathematical Journal 15 (1992), 354–374.
• 93-1. Order and type as measures of growth for convex or entire functions. Proceedings of the London Mathematical Society (3) 66 (1993), 152–186.
• 02-1. A semigroup of operators in convexity theory. Transactions of the American Mathematical Society 354 (2002), 2035–2053. DVI (154 kB) - PS (343 kB) - PDF (221 kB). The semigroup studied in this paper has three generators and 18 elements. Ganna Kudryavtseva and Volodymyr Mazorchuk have studied similar semigroups with more than three generators in their paper On Kiselman's semigroup.

Mathematical problems in image analysis

• 96-2. Regularity of distance transformations in image analysis. Computer Vision and Image Understanding 64 (1996), 390–398. DVI - PS - PDF.

Shape description

• 05-2. Subharmonic functions on discrete structures. Harmonic Analysis, Signal Processing, and Complexity. Festschrift in Honor of the 60th birthday of Carlos A. Berenstein,, pp. 67–80. Progress in Mathematics, Vol. 238. Irene Sabadini; Daniele C. Struppa; David F. Walnut, Eds., 2005, xi + 162 pp. ISBN: 0-8176-4358-3. Boston, Basel, Berlin: Birkhäuser.

History of geometry

• 2012-04-24. Euclid's straight lines, 25 pages.

Analysis in several complex variables and complex geometry

• 96-1. Lineally convex Hartogs domains. Acta Mathematica Vietnamica 21 (1996), No. 1, 69–94. DVI - PS - PDF.
• 97-1. Duality of functions defined in lineally convex sets. Universitatis Iagellonicae Acta Mathematica, 35 (1997), 7–36. DVI - PS - PDF.
• 98-1. A differential inequality characterizing weak lineal convexity. Mathematische Annalen 311 (1998), 1–10. DVI - PS - PDF.
• 00-1. Ensembles de sous-niveau et images inverses des fonctions plurisousharmoniques. Bulletin des Sciences Mathématiques 124 (2000), 75–92. DVI - PS - PDF.
• 00-2. Plurisubharmonic functions and potential theory in several complex variables. This is an article on the history of plurisubharmonic functions. It is a contribution to the book project Development of mathematics during the second half of the XXth century, edited by Jean-Paul Pier. Birkhäuser 2000. DVI - PS - PDF.
• 05-1. Functions on discrete sets holomorphic in the sense of Isaacs, or monodiffric functions of the first kind. Science in China, Series A, Mathematics, 48 Supplement (2005), 1–11.
• 08-3. Functions on discrete sets holomorphic in the sense of Ferrand, or monodiffric functions of the second kind. Science in China, Series A, Mathematics, April 2008, 51, No. 4, 604–619. The article is available at www.scichina.com and www.springerlink.com.
• 11-2. Les mathématiques de Nguyen Thanh Van. Actes du colloque "Analyse Complexe et Applications" en l'honneur de Nguyen Thanh Van. Annales de la Faculté des Sciences de Toulouse, Mathématiques, (6), 20, Fascicule Spécial, 19–32.
• 11-3. Analytic continuation of fundamental solutions to differential equations with constant coefficients. Actes du colloque "Analyse Complexe et Applications" en l'honneur de Nguyen Thanh Van. Annales de la Faculté des Sciences de Toulouse, Mathématiques, (6), 20, Fascicule Spécial, 153–182.

Distribution Theory and Fourier Analysis

• 02-2. Generalized Fourier transformations: the work of Bochner and Carleman viewed in the light of the theories of Schwartz and Sato. In: Microlocal Analysis and Complex Fourier Analysis, pp. 166–185. (Eds. Takahiro Kawai, Keiko Fujita.) Singapore: World Scientific, 2002.
• 07-1. Enkonduko al distribucioj. Acta Sanmarinensia, Vol. VI, No. 4, pp. 105–132 (2004). Academiae Internationalis Scientiarum (AIS). Göttingen: Leins Verlag, 2007.

Linguistics

• 95-a. Transitivaj kaj netransitivaj verboj en Esperanto. Stato kaj Estonteco de la Internacia Lingvo Esperanto (Ed. P. Chrdle). Proceedings of the First Symposium of the Academy of Esperanto, Prague, July, 1994, pp. 24–40. Prague: Kava-Pech, 1995. DVI - PS - PDF.
• 95-b. Vad är ett naturligt tal? Ett exempel på matematisk språkvård [What is a natural number? An example of mathematical language planning]. Språk och Stil, tidskrift för svensk språkforskning 4 [1994] (1995), 133–143. DVI - PS - PDF.
• 01-a. La sveda faklingvo en tekniko, matematiko kaj natursciencoj. In: Fiedler, Sabine; Liu Haitao (Eds.): Studoj pri interlingvistiko. Festlibro oma^ge al la 60-jari^go de Detlev Blanke. Studien zur Interlingvistik. Festschrift für Detlev Blanke zum 60. Geburtstag, pp. 40–56. Dobrichovice (Prague): Kava-Pech, 2001. DVI (64 kB) - PS (337 kB) - PDF (207 kB).
• 01-b. Kreado de matematikaj terminoj. In: Christer Kiselman; Geraldo Mattos (Eds.): Lingva Planado kaj Leksikologio. Language Planning and Lexicology, pp. 173–187. Proceedings of an international symposium held in Zagreb, 2001 07 28—30, 9 pp. Chapecó-SC: Fonto, 2001. DVI (41 kB) - PS (232 kB) - PDF (143 kB).
• 01-c. Svenskt fackspråk inom teknik, matematik och naturvetenskap [The situation of Swedish in the fields of technology, mathematics, and the natural sciences]. Libens Merito. Festskrift till Stig Strömholm, pp. 225–243. Acta Academiæ Regiæ Scientiarum Upsaliensis 21 (2001). DVI (92 kB) - PS (332 kB) - PDF (194 kB).
• 2004-06-05. Språkpolitik för en teknisk-naturvetenskaplig fakultet. Underlag för ett föredrag vid konferensen om parallellspråkighet på Voksenåsen 2004-06-07—08. [Language planning for a Faculty of Science and Technology. In Swedish.]
• 08-a. Esperanto: its origins and early history. In: Prace Komisji Spraw Europejskich PAU. Tom II, pp. 39–56. Ed. Andrzej Pelczar. Kraków: Polska Akademia Umiejetnosci, 2008, 79 pp.
• 08-b. Christer Kiselman; Lars Mouwitz. Matematiktermer för skolan [Mathematical Terms for School Use]. Göteborg: Göteborg University, National Center for Mathematics Education. 312 pp. (The link goes to the pdf file of the second printing, May 2009.)
• 08-c. Språkens rikedomar och terminologins problem [The treasures of the languages and the problems of terminology]. In: Christer Kiselman; Lars Mouwitz, Matematiktermer för skolan [Mathematical Terms for School Use], pp. 287–292. Göteborg: Göteborg University, National Center for Mathematics Education.
• 11-a. Variantoj de esperanto iniciatitaj de Zamenhof. Esperantologio / Esperanto Studies 5, 79–149. Published electronically 2011-06-24; on paper 2011-07-23. Also published in Esperanto, komenco, aktualo kaj estonteco. Aktoj de la 33-a Esperantologia Konferenco en la 95-a Universala Kongreso de Esperanto, Havano 2010, pp. 45–107. Rotterdam: Universala Esperanto-Asocio. Published 2011-07-23.

I will be happy to send copies of any of these articles if you are interested.