Christer Oscar Kiselman's research interests

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

Digital geometry, mathematical morphology, and discrete optimization

• 00-3. Digital Jordan curve theorems.
• 03-1. La geometrio de la komputila ekrano.
• 04-1. Convex functions on discrete sets.
• 04-2. Digital Geometry and Mathematical Morphology. Abstract.
• 05-2. Subharmonic functions on discrete structures.
• 07-2. Division of mappings between complete lattices.
• 08-1. Minima locaux, fonctions marginales et hyperplans séparants dans l'optimisation discrète.
• 08-2. Datorskärmens geometri [The geometry of the computer screen].
• 10-1. Characterizing digital straightness by means of difference operators.
• 10-2. Inverses and quotients of mappings between ordered sets.
• 10-3. Local minima, marginal functions, and separating hyperplanes in discrete optimization.
• 10-4. Christer O. Kiselman; Shiva Samieinia, Convexity of marginal functions in the discrete case.
• 11-1. Characterizing digital straightness and digital convexity by means of difference operators.
• 13-1. Diskreta kaj reela optimumado.
• 14-1. Kiel rekoni rektojn kaj strekojn inter ĉiuj kurboj kaj aliaj bildoj sur la komputila ekrano?
• 15-2. Estimates for solutions to discrete convolution equations.
• 18-2. Digita geometrio, matematika morfologio kaj diskreta optimumado, 69 pp.
• 2019-04-30. Duality: A tool for shape description. Manuscript, 19 pp., accepted for publication.
• 22-1. Elements of Digital Geometry, Mathematical Morphology, and Discrete Optimization, comprising 488 pages, published on 2022 January 18 by World Scientific, Singapore.
• 22-2. Generalized elementary functions. Published online 2022 February 17.

Convexity theory

• 92-2. Regularity classes for operations in convexity theory.
• 93-1. Order and type as measures of growth for convex or entire functions.
• 96-2. Regularity of distance transformations in image analysis.
• 02-1. A semigroup of operators in convexity theory.
• 10-4. Kiselman, Christer O.; Samieinia, Shiva. Convexity of marginal functions in the discrete case.
• 17-5. Kiselman, Christer O.; Samieinia, Shiva. Convexity of marginal functions in the discrete case.
• 17-6. Discrete convolution operators, the Fourier transformation, and its tropical counterpart: the Fenchel transformation.

Analysis in several complex variables and complex geometry

• 96-1. Lineally convex Hartogs domains.
• 97-1. Duality of functions defined in lineally convex sets.
• 98-1. A differential inequality characterizing weak lineal convexity.
• 00-1. Ensembles de sous-niveau et images inverses des fonctions plurisousharmoniques.
• 00-2. Plurisubharmonic functions and potential theory in several complex variables.
• 05-1. Functions on discrete sets holomorphic in the sense of Isaacs, or monodiffric functions of the first kind.
• 08-3. Functions on discrete sets holomorphic in the sense of Ferrand, or monodiffric functions of the second kind.
• 09-1. Vyacheslav Zakharyuta's complex analysis.
• 11-2. Les mathématiques de Nguyen Thanh Van.
• 11-3. Analytic continuation of fundamental solutions to differential equations with constant coefficients.
• 16-1. Weak lineal convexity.
• 17-2. Domains of holomorphy for Fourier transforms of solutions to discrete convolution equations.
• 19-1. Generalized convexity: The case of lineally convex Hartogs domains
• 2021-11-19. Complex Convexity, a chapter in Handbook of Complex Analysis, edited by Steven Krantz.

History of mathematics

• 15-1. Euclid's straight lines.
• 19-i. Werner Fenchel, a pioneer in convexity theory and a migrant scientist.
• 19-ii. Hans Rådström and how to define smooth functions on any set.

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.
• 07-1. Enkonduko al distribucioj.

Linguistics

• 95-a. Transitivaj kaj netransitivaj verboj en Esperanto.
• 95-b. Vad är ett naturligt tal? Ett exempel på matematisk språkvård [What is a natural number? An example of mathematical language planning].
• 01-a. La sveda faklingvo en tekniko, matematiko kaj natursciencoj.
• 01-b. Kreado de matematikaj terminoj.
• 01-c. Svenskt fackspråk inom teknik, matematik och naturvetenskap [The situation of Swedish in the fields of technology, mathematics, and the natural sciences].
• 08-a. Esperanto: its origins and early history.
• 08-b. Christer Kiselman; Lars Mouwitz. Matematiktermer för skolan [Mathematical Terms for School Use].
• 08-c. Språkens rikedomar och terminologins problem [The treasures of the languages and the problems of terminology].
• 11-a. Variantoj de esperanto iniciatitaj de Zamenhof.
• 16-b. La jidogramatiko de Zamenhof kaj lia Lingvo universala.
• 18-i. Enkonduko. In: Kiselman, Christer Oscar; Corsetti, Renato; Dasgupto, Probal, Eds. Aliroj al esperanto, pp. 5–8.
• 19-a. Language choice in scientific writing: The case of mathematics at Uppsala University and a Nordic journal.
• 19-b. Kion faris Zamenhof antaŭ 1887?
• 22-a. Zamenhof's Yiddish Grammar and His Universal Language: Two Projects in Ashkenazi Culture, 167 pp. Published in 2022 by KAVA-PECH, Dobřichovice.

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